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A sturdy aluminum spool and a digital gear design for $20. This is a great reel to start off hitting lakes and ponds. Daiwa reels are known and respected for being affordable, well made, reliable ...

Best Daiwa Reels of 2023

ThoughtSpot Product Innovation Powers New Wave of Growth With the strategic acquisition of Mode Analytics, ThoughtSpot has further diversified its position as a multi-product company, now serving a wider array of customer personas and delivering a comprehensible platform for all needs. In addition, in the last twelve months, ThoughtSpot:

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Goldcast

goldcast

Kingstown, St. Vincent and the Grenadines, December 17th, 2024/Chainwire/--MINGO, a digital wallet built on the Hedera Hashgraph network, introduces an NFT-based Programmable Digital Ticketing (PDT) system to innovate the ticketing industry. By addressing critical issues such as fraud, scalping, and resale inefficiencies, MINGO delivers a secure and transparent solution trusted by leading names in sports and entertainment. MINGO’s native token $MINGO is set to go live on Coinstore on Wednesday, December 18th, and more exchanges including BitMart by the end of the year, marking another milestone in MINGO's mission to drive Web3 adoption. Trusted by Industry Leaders World Boxing Council (WBC)
Fight Circus
NUCA MMA
Comic-Con Ireland
Tyson Fury
Goldstar Promotions
Hedera
World Boxing Muay Thai - (WBC Muay Thai )
Yucateco Boxing League These collaborations highlight MINGO’s scalability for large-scale events while enhancing the experience for both organizers and fans. Key Features of MINGO Tickets For Event Organizers: Fraud Prevention: Hedera Hashgraph ensures each ticket is tamper-proof, effectively eliminating counterfeits and scams.
Anti-Scalping Measures: Price caps on resales ensure fair access for fans.
Additional Revenue: Secondary sales generate commissions for event organizers.
Seamless Delivery: Tickets are securely delivered and managed in the MINGO Wallet. For Attendees : Exclusive Perks: NFT tickets can include VIP upgrades, gifts from organizers, and meet-and-greets.
Collectible Digital Memories: Fans receive digital keepsakes tied to the event, such as messages from artists or highlights.
Enhanced Utility: Tickets can unlock bonus content or additional event experiences before, during, or after the show.
Secure Resales: Transparent resale systems ensure fairness and eliminate scalping. Built on Hedera – Security, Efficiency, and Sustainability Powered by the Hedera Hashgraph network, MINGO’s ticketing system benefits from Hedera’s low fees, high-speed transactions, and energy efficiency. As an early adopter, MINGO has been working with Hedera since 2018 demonstrating its long-term commitment to the network and the Web3 space. Driving Innovation in Ticketing MINGO’s NFT Ticketing System combines practical, real-world applications with blockchain technology, offering benefits that traditional systems cannot match. By eliminating fraud, protecting fans, and creating new value opportunities, MINGO is setting the standard for event ticketing. “We’re honoured to work with leaders across sports and entertainment to address the challenges of ticketing,” said Joe Arthur, CEO of MINGO. “Our NFT-based system isn’t just about tickets—it’s about delivering unforgettable experiences to fans while adding value for organizers.” About MINGO MINGO is a digital wallet and NFT ticketing solution built on the Hedera Hashgraph network. Operating since 2018, MINGO offers secure, programmable digital tickets that eliminate fraud, protect fans, and generate value for event organizers. Trusted by leading organizations such as the WBC, Fight Circus, and Comic-Con Ireland, MINGO is redefining ticketing for the digital age. Website - mingo.com X - https://x.com/mingoapps?s=21 Telegram- https://t.me/+vcB2K-OQF6sxOTBk Whitepaper - https://mingo-1.gitbook.io/mingo Contact Marketing Manager Cillian Arthur MINGO cillian@mingoapps.com This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here Kingstown, St. Vincent and the Grenadines, December 17th, 2024/Chainwire/--MINGO, a digital wallet built on the Hedera Hashgraph network, introduces an NFT-based Programmable Digital Ticketing (PDT) system to innovate the ticketing industry. By addressing critical issues such as fraud, scalping, and resale inefficiencies, MINGO delivers a secure and transparent solution trusted by leading names in sports and entertainment. MINGO’s native token $MINGO is set to go live on Coinstore on Wednesday, December 18th, and more exchanges including BitMart by the end of the year, marking another milestone in MINGO's mission to drive Web3 adoption. Trusted by Industry Leaders World Boxing Council (WBC) Fight Circus NUCA MMA Comic-Con Ireland Tyson Fury Goldstar Promotions Hedera World Boxing Muay Thai - (WBC Muay Thai ) Yucateco Boxing League World Boxing Council (WBC) Fight Circus NUCA MMA Comic-Con Ireland Tyson Fury Goldstar Promotions Hedera World Boxing Muay Thai - (WBC Muay Thai ) Yucateco Boxing League These collaborations highlight MINGO’s scalability for large-scale events while enhancing the experience for both organizers and fans. Key Features of MINGO Tickets For Event Organizers: Fraud Prevention: Hedera Hashgraph ensures each ticket is tamper-proof, effectively eliminating counterfeits and scams. Anti-Scalping Measures: Price caps on resales ensure fair access for fans. Additional Revenue: Secondary sales generate commissions for event organizers. Seamless Delivery: Tickets are securely delivered and managed in the MINGO Wallet. Fraud Prevention: Hedera Hashgraph ensures each ticket is tamper-proof, effectively eliminating counterfeits and scams. Anti-Scalping Measures: Price caps on resales ensure fair access for fans. Additional Revenue: Secondary sales generate commissions for event organizers. Seamless Delivery: Tickets are securely delivered and managed in the MINGO Wallet. For Attendees : Exclusive Perks: NFT tickets can include VIP upgrades, gifts from organizers, and meet-and-greets. Collectible Digital Memories: Fans receive digital keepsakes tied to the event, such as messages from artists or highlights. Enhanced Utility: Tickets can unlock bonus content or additional event experiences before, during, or after the show. Secure Resales: Transparent resale systems ensure fairness and eliminate scalping. Exclusive Perks: NFT tickets can include VIP upgrades, gifts from organizers, and meet-and-greets. Collectible Digital Memories: Fans receive digital keepsakes tied to the event, such as messages from artists or highlights. Enhanced Utility: Tickets can unlock bonus content or additional event experiences before, during, or after the show. Secure Resales: Transparent resale systems ensure fairness and eliminate scalping. Built on Hedera – Security, Efficiency, and Sustainability Powered by the Hedera Hashgraph network, MINGO’s ticketing system benefits from Hedera’s low fees, high-speed transactions, and energy efficiency. As an early adopter, MINGO has been working with Hedera since 2018 demonstrating its long-term commitment to the network and the Web3 space. Driving Innovation in Ticketing MINGO’s NFT Ticketing System combines practical, real-world applications with blockchain technology, offering benefits that traditional systems cannot match. By eliminating fraud, protecting fans, and creating new value opportunities, MINGO is setting the standard for event ticketing. “We’re honoured to work with leaders across sports and entertainment to address the challenges of ticketing,” said Joe Arthur, CEO of MINGO. “We’re honoured to work with leaders across sports and entertainment to address the challenges of ticketing,” said Joe Arthur, CEO of MINGO. “Our NFT-based system isn’t just about tickets—it’s about delivering unforgettable experiences to fans while adding value for organizers.” “Our NFT-based system isn’t just about tickets—it’s about delivering unforgettable experiences to fans while adding value for organizers.” About MINGO MINGO is a digital wallet and NFT ticketing solution built on the Hedera Hashgraph network. Operating since 2018, MINGO offers secure, programmable digital tickets that eliminate fraud, protect fans, and generate value for event organizers. MINGO MINGO Trusted by leading organizations such as the WBC, Fight Circus, and Comic-Con Ireland, MINGO is redefining ticketing for the digital age. Website - mingo.com mingo.com mingo.com X - https://x.com/mingoapps?s=21 https://x.com/mingoapps?s=21 https://x.com/mingoapps?s=21 Telegram- https://t.me/+vcB2K-OQF6sxOTBk https://t.me/+vcB2K-OQF6sxOTBk https://t.me/+vcB2K-OQF6sxOTBk Whitepaper - https://mingo-1.gitbook.io/mingo https://mingo-1.gitbook.io/mingo https://mingo-1.gitbook.io/mingo Contact Marketing Manager Cillian Arthur MINGO cillian@mingoapps.com This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here here here

MINGO, Hedera Based Wallet, Sets Sights On The Global Ticketing Industry

MINGO, Hedera əsaslı pul kisəsi, Qlobal Bilet Sənayesinə Baxışlar Aparır

MINGO, базиран на Hedera портфейл, насочва вниманието си към глобалната индустрия за продажба на билети

MINGO, la billetera basada en Hedera, apunta a la industria global de venta de entradas

MINGO, Hedera-pohjainen lompakko, asettaa huomion maailmanlaajuiselle lipputeollisuudelle

MINGO, a carteira baseada en Hedera, pon a vista na industria global de billetes

ヘデラベースのウォレットMINGOが世界のチケット業界に照準を合わせる

MINGO, Hedera-ზე დაფუძნებული საფულე, ასახავს გლობალურ ბილეთების ინდუსტრიას

MINGO, Hederos piniginė, atkreipia dėmesį į pasaulinę bilietų pardavimo pramonę

MINGO, паричник базиран на Хедера, поставува поглед на глобалната индустрија за билети

मिंगो, हेडेरामा आधारित वालेट, ग्लोबल टिकटिङ उद्योगमा स्थानहरू सेट गर्दछ

MINGO, Hedera-baserad plånbok, sätter sikte på den globala biljettbranschen

MINGO, Ví điện tử Hedera, hướng đến ngành công nghiệp bán vé toàn cầu

New Findings Show All Major Art Protection Tools Are Vulnerable to AI Forgery

Author:
(1) David Staines. Table of Links Abstract 1 Introduction 2 Mathematical Arguments 3 Outline and Preview 4 Calvo Framework and 4.1 Household’s Problem 4.2 Preferences 4.3 Household Equilibrium Conditions 4.4 Price-Setting Problem 4.5 Nominal Equilibrium Conditions 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.8 Recursive Equilibrium 5 Existing Solutions 5.1 Singular Phillips Curve 5.2 Persistence and Policy Puzzles 5.3 Two Comparison Models 5.4 Lucas Critique 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6.2 Equilibrium Construction 6.3 Literature Comparison 6.4 Equilibrium Analysis 7 General Linearized Phillips Curve 7.1 Slope Coefficients 7.2 Error Coefficients 8 Existence Results and 8.1 Main Results 8.2 Key Proofs 8.3 Discussion 9 Bifurcation Analysis 9.1 Analytic Aspects 9.2 Algebraic Aspects (I) Singularities and Covers 9.3 Algebraic Aspects (II) Homology 9.4 Algebraic Aspects (III) Schemes 9.5 Wider Economic Interpretations 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10.2 Econometric Duality 10.3 Coefficient Properties 10.4 Microeconomic Interpretation 11 Policy Rule 12 Conclusions and References Appendices A Proof of Theorem 2 and A.1 Proof of Part (i) A.2 Behaviour of ∆ A.3 Proof Part (iii) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.3 Price Dispersion (4.5) B.4 Cost Minimization (4.6) and (10.4) B.5 Consolidation (4.8) C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C.2 Extending No Persistence D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D.2 Profits and Long-Run Growth E Slopes and Eigenvalues and E.1 Slope Coefficients E.2 Linearized DSGE Solution E.3 Eigenvalue Conditions E.4 Rouche’s Theorem Conditions F Abstract Algebra and F.1 Homology Groups F.2 Basic Categories F.3 De Rham Cohomology F.4 Marginal Costs and Inflation G Further Keynesian Models and G.1 Taylor Pricing G.2 Calvo Wage Phillips Curve G.3 Unconventional Policy Settings H Empirical Robustness and H.1 Parameter Selection H.2 Phillips Curve I Additional Evidence and I.1 Other Structural Parameters I.2 Lucas Critique I.3 Trend Inflation Volatility F.3 De Rham Cohomology This last mathematical stanza seeks to explain the power of the linear approximation in the most general setting, with a view to justifying major results in the text. This includes the linearization step from (3)-(5) and Decomposition 1, specific to Calvo, and the general bifurcation result Theorem 7. The first subsubsection sets out preliminaries of differential topology and cohomology. The second states the main result. The best textbook here is probably Tu [2011]; some readers may find the informal presentation in Stone and Goldbart [2009] helpful. F.3.1 Preliminaries denote the intersection of domains by and its map by the two chart maps to the two images It follows that the transition map between the two charts is the map between the two images of this intersection under the two chart maps. A Differential Form is a coordinate-independent approach to calculus. It has its roots in physics (see Stone and Goldbart [2009]). It differs from the approach to integration in the rest of the paper because it is orientation-dependent, so integrals can be zero or negative for non-zero functions. In general, for a differential form ω integrated over a manifold M and the same manifold but with opposite orientation M′ then A k form is an object that can be integrated over a k dimensional oriented manifold and is homogeneous of degree k in the coordinate differentials. A one form can be integrated over an oriented interval [a, b] in the domain of f: Similarly, the expression f(x, y, z) dx ∧ dy + g(x, y, z) dz ∧ dx + h(x, y, z) dy ∧ dz is a 2-form, that has the following integral over an oriented surface S likewise, the 3-form f(x, y, z) dx∧dy∧dz is called a volume element, integrated over an oriented region of three dimensional space. ∧ is called the wedge or Exterior Product. It is an alternating product, in the sense that The exterior derivative operator d sends k forms to k+1 forms, so perimeters go to areas, surface areas to enclosed volumes etc. [120] The generalized Stokes theorem states that the integral of a differential form ω over the boundary of some orientable manifold Ω equals the integral of its exterior derivative. This means that the volume of a sphere is equal to the surface area of the family of spheres covering the circle, as their diameters become arbitrarily small. In general, we can approximate the integral over k + 1- form arbitrarily well, by summing over the boundary of its k form. This constitutes a deep extension of the fundamental theorem of calculus. Lastly, returning to algebraic topology, it is necessary to introduce Cohomology in general, specifically the Singular Cohomology. Cohomology is the dual construction to homology. It arises from Cochains, which are functions defined on the group of chains in homology theory. Cohomology develops from the geometry of functions and their pullbacks. Taking two spaces X and Y and a function F on Y , any mapping f : X → Y will lead to another F ◦f called the pullback of F on X under f. Typically, there is interest in the relation between continuity and differentiability properties of the functions. Leading cohomology theories have a product called the Cup Product, which gives them a ring structure. For this reason cohomology can provide richer algebraic invariants. The singular cohomology is a powerful topological invariant, associating a graded-commutative ring to any topological space.121 Decomposition 1 exemplifies this structure. Every continuous map f : X → Y creates a homomorphism from the cohomology ring of Y to that of X; this puts strong restrictions on the behavior of maps between the two spaces. Many properties of cohomology are only minor variants of homology: • Two homotopic maps from X to Y induce the same homomorphism on cohomology (as they do on homology.) • If a space X is the union of open subsets U and V , then there is a long exact sequence Informally, these properties allow cohomology calculations to be broken down over suitable partitions. On the other hand, cohomology has a special structure absent in homology. For any topological space X and commutative ring R, there is a bilinear123 map called the Cup Product. F.3.2 Formalization and Application The De Rham Cohomology is a technique common to both algebraic and differential topology. It is a powerful tool capable of expressing basic topological information about smooth manifolds, making it easy to compute concrete representations of cohomology classes. It is a cohomology theory based on the behavior of differential forms. The key distinction is between exact and closed forms. Here, an Exact Form is is a differential form α, that is the exterior derivative of another differential form β, whilst a closed form is a differential form α whose exterior derivative is zero (dα = 0). Thus an exact form is an image of d and a closed form is a kernel of d. Every exact form is closed but a closed form need not be exact. [125] Poincaré’s lemma ensures it is true for contractible spaces. However, there is a critical connection between the existence of exactness and the existence of holes. From this standpoint, the De Rham cohomology measures how the Fundamental Theorem of Calculus [126] fails on general manifolds in higher dimensions. The De Rham complex is the cochain complex of differential forms on a smooth manifold M with the exterior as its differential: The exterior product endows the direct sum of groups with a ring structure. A further consequence of the theorem is that two cohomology rings are isomorphic, when viewed as graded rings, where the analagous product for the singular cohomology is the cup product. At last, we come to the application, the cohomology computation for our main model. Proposition 32. The Calvo Phillips curve model has the following De Rham cohomology representations In conjunction with Theorem 9, this formally justifies the use of the linear approximations (3)-(5) to represent the non-binding constraint on the representative firm or social planner. This paper is available on arxiv under CC 4.0 license. Author: (1) David Staines. Author: Author: (1) David Staines. Table of Links Abstract Abstract 1 Introduction 1 Introduction 2 Mathematical Arguments 2 Mathematical Arguments 3 Outline and Preview 3 Outline and Preview 4 Calvo Framework and 4.1 Household’s Problem 4 Calvo Framework and 4.1 Household’s Problem 4.2 Preferences 4.2 Preferences 4.3 Household Equilibrium Conditions 4.3 Household Equilibrium Conditions 4.4 Price-Setting Problem 4.4 Price-Setting Problem 4.5 Nominal Equilibrium Conditions 4.5 Nominal Equilibrium Conditions 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.6 Real Equilibrium Conditions and 4.7 Shocks 4.8 Recursive Equilibrium 4.8 Recursive Equilibrium 5 Existing Solutions 5 Existing Solutions 5.1 Singular Phillips Curve 5.1 Singular Phillips Curve 5.2 Persistence and Policy Puzzles 5.2 Persistence and Policy Puzzles 5.3 Two Comparison Models 5.3 Two Comparison Models 5.4 Lucas Critique 5.4 Lucas Critique 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems 6.2 Equilibrium Construction 6.2 Equilibrium Construction 6.3 Literature Comparison 6.3 Literature Comparison 6.4 Equilibrium Analysis 6.4 Equilibrium Analysis 7 General Linearized Phillips Curve 7 General Linearized Phillips Curve 7.1 Slope Coefficients 7.1 Slope Coefficients 7.2 Error Coefficients 7.2 Error Coefficients 8 Existence Results and 8.1 Main Results 8 Existence Results and 8.1 Main Results 8.2 Key Proofs 8.2 Key Proofs 8.3 Discussion 8.3 Discussion 9 Bifurcation Analysis 9 Bifurcation Analysis 9.1 Analytic Aspects 9.1 Analytic Aspects 9.2 Algebraic Aspects (I) Singularities and Covers 9.2 Algebraic Aspects (I) Singularities and Covers 9.3 Algebraic Aspects (II) Homology 9.3 Algebraic Aspects (II) Homology 9.4 Algebraic Aspects (III) Schemes 9.4 Algebraic Aspects (III) Schemes 9.5 Wider Economic Interpretations 9.5 Wider Economic Interpretations 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs 10.2 Econometric Duality 10.2 Econometric Duality 10.3 Coefficient Properties 10.3 Coefficient Properties 10.4 Microeconomic Interpretation 10.4 Microeconomic Interpretation 11 Policy Rule 11 Policy Rule 12 Conclusions and References 12 Conclusions and References Appendices Appendices A Proof of Theorem 2 and A.1 Proof of Part (i) A Proof of Theorem 2 and A.1 Proof of Part (i) A.2 Behaviour of ∆ A.2 Behaviour of ∆ A.3 Proof Part (iii) A.3 Proof Part (iii) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B Proofs from Section 4 and B.1 Individual Product Demand (4.2) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.2 Flexible Price Equilibrium and ZINSS (4.4) B.3 Price Dispersion (4.5) B.3 Price Dispersion (4.5) B.4 Cost Minimization (4.6) and (10.4) B.4 Cost Minimization (4.6) and (10.4) B.5 Consolidation (4.8) B.5 Consolidation (4.8) C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence C.2 Extending No Persistence C.2 Extending No Persistence D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium D.2 Profits and Long-Run Growth D.2 Profits and Long-Run Growth E Slopes and Eigenvalues and E.1 Slope Coefficients E Slopes and Eigenvalues and E.1 Slope Coefficients E.2 Linearized DSGE Solution E.2 Linearized DSGE Solution E.3 Eigenvalue Conditions E.3 Eigenvalue Conditions E.4 Rouche’s Theorem Conditions E.4 Rouche’s Theorem Conditions F Abstract Algebra and F.1 Homology Groups F Abstract Algebra and F.1 Homology Groups F.2 Basic Categories F.2 Basic Categories F.3 De Rham Cohomology F.3 De Rham Cohomology F.4 Marginal Costs and Inflation F.4 Marginal Costs and Inflation G Further Keynesian Models and G.1 Taylor Pricing G Further Keynesian Models and G.1 Taylor Pricing G.2 Calvo Wage Phillips Curve G.2 Calvo Wage Phillips Curve G.3 Unconventional Policy Settings G.3 Unconventional Policy Settings H Empirical Robustness and H.1 Parameter Selection H Empirical Robustness and H.1 Parameter Selection H.2 Phillips Curve H.2 Phillips Curve I Additional Evidence and I.1 Other Structural Parameters I Additional Evidence and I.1 Other Structural Parameters I.2 Lucas Critique I.2 Lucas Critique I.3 Trend Inflation Volatility I.3 Trend Inflation Volatility F.3 De Rham Cohomology This last mathematical stanza seeks to explain the power of the linear approximation in the most general setting, with a view to justifying major results in the text. This includes the linearization step from (3)-(5) and Decomposition 1, specific to Calvo, and the general bifurcation result Theorem 7. The first subsubsection sets out preliminaries of differential topology and cohomology. The second states the main result. The best textbook here is probably Tu [2011]; some readers may find the informal presentation in Stone and Goldbart [2009] helpful. F.3.1 Preliminaries F.3.1 Preliminaries denote the intersection of domains by and its map by the two chart maps to the two images It follows that the transition map between the two charts is the map between the two images of this intersection under the two chart maps. A Differential Form is a coordinate-independent approach to calculus. It has its roots in physics (see Stone and Goldbart [2009]). It differs from the approach to integration in the rest of the paper because it is orientation-dependent, so integrals can be zero or negative for non-zero functions. In general, for a differential form ω integrated over a manifold M and the same manifold but with opposite orientation M′ then Differential Form A k form is an object that can be integrated over a k dimensional oriented manifold and is homogeneous of degree k in the coordinate differentials. A one form can be integrated over an oriented interval [a, b] in the domain of f: Similarly, the expression f(x, y, z) dx ∧ dy + g(x, y, z) dz ∧ dx + h(x, y, z) dy ∧ dz is a 2-form, that has the following integral over an oriented surface S likewise, the 3-form f(x, y, z) dx∧dy∧dz is called a volume element, integrated over an oriented region of three dimensional space. ∧ is called the wedge or Exterior Product . It is an alternating product, in the sense that Exterior Product The exterior derivative operator d sends k forms to k+1 forms, so perimeters go to areas, surface areas to enclosed volumes etc. [120] The generalized Stokes theorem states that the integral of a differential form ω over the boundary of some orientable manifold Ω equals the integral of its exterior derivative. This means that the volume of a sphere is equal to the surface area of the family of spheres covering the circle, as their diameters become arbitrarily small. In general, we can approximate the integral over k + 1- form arbitrarily well, by summing over the boundary of its k form. This constitutes a deep extension of the fundamental theorem of calculus. Lastly, returning to algebraic topology, it is necessary to introduce Cohomology in general, specifically the Singular Cohomology . Cohomology is the dual construction to homology. It arises from Cochains , which are functions defined on the group of chains in homology theory. Cohomology Singular Cohomology Cochains Cohomology develops from the geometry of functions and their pullbacks. Taking two spaces X and Y and a function F on Y , any mapping f : X → Y will lead to another F ◦f called the pullback of F on X under f. Typically, there is interest in the relation between continuity and differentiability properties of the functions. Leading cohomology theories have a product called the Cup Product, which gives them a ring structure. For this reason cohomology can provide richer algebraic invariants. The singular cohomology is a powerful topological invariant, associating a graded-commutative ring to any topological space.121 Decomposition 1 exemplifies this structure. Every continuous map f : X → Y creates a homomorphism from the cohomology ring of Y to that of X; this puts strong restrictions on the behavior of maps between the two spaces. Many properties of cohomology are only minor variants of homology: • Two homotopic maps from X to Y induce the same homomorphism on cohomology (as they do on homology.) • If a space X is the union of open subsets U and V , then there is a long exact sequence Informally, these properties allow cohomology calculations to be broken down over suitable partitions. On the other hand, cohomology has a special structure absent in homology. For any topological space X and commutative ring R, there is a bilinear123 map called the Cup Product. F.3.2 Formalization and Application F.3.2 Formalization and Application The De Rham Cohomology is a technique common to both algebraic and differential topology. It is a powerful tool capable of expressing basic topological information about smooth manifolds, making it easy to compute concrete representations of cohomology classes. It is a cohomology theory based on the behavior of differential forms. The key distinction is between exact and closed forms. Here, an Exact Form is is a differential form α, that is the exterior derivative of another differential form β, whilst a closed form is a differential form α whose exterior derivative is zero (dα = 0). Thus an exact form is an image of d and a closed form is a kernel of d. Every exact form is closed but a closed form need not be exact. [125] Poincaré’s lemma ensures it is true for contractible spaces. However, there is a critical connection between the existence of exactness and the existence of holes. From this standpoint, the De Rham cohomology measures how the Fundamental Theorem of Calculus [126] fails on general manifolds in higher dimensions. The De Rham complex is the cochain complex of differential forms on a smooth manifold M with the exterior as its differential: The exterior product endows the direct sum of groups with a ring structure. A further consequence of the theorem is that two cohomology rings are isomorphic, when viewed as graded rings, where the analagous product for the singular cohomology is the cup product. At last, we come to the application, the cohomology computation for our main model. Proposition 32. The Calvo Phillips curve model has the following De Rham cohomology representations In conjunction with Theorem 9, this formally justifies the use of the linear approximations (3)-(5) to represent the non-binding constraint on the representative firm or social planner. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

A Simple Guide to De Rham Cohomology and Its Mathematical Applications

Authors:
(1) Diptarka Chakraborty, National University of Singapore, Singapore
(2) Sourav Chakraborty, Indian Statistical Institute, Kolkata;
(3) Gunjan Kumar, National University of Singapore, Singapore;
(4) Kuldeep S. Meel, University of Toronto, Toronto. Table of Links Abstract and 1 Introduction 2 Notations and Preliminaries 3 Related Work 4 An Efficient One-Round Adaptive Algorithm and 4.1 High-Level Overview 4.2 Algorithm Description 4.3 Technical Analysis 5 Conclusion 6 Acknowledgements and References A Missing Proofs B An O(log log n)-query fully adaptive algorithm 6 Acknowledgements We thank the anonymous reviewers for their useful comments. D. Chakraborty is supported in part by an MoE AcRF Tier 2 grant (MOE-T2EP20221-0009), an MoE AcRF Tier 1 grant (T1 251RES2303), and a Google South & South-East Asia Research Award. K. S. Meel is supported in part by National Research Foundation Singapore under its NRF Fellowship Programme [NRF-NRFFAI1-2019-0004 ], Ministry of Education Singapore Tier 2 grant MOE-T2EP20121-0011, and Ministry of Education Singapore Tier 1 Grant [R-252-000-B59-114]. References [AAAK17] Arpit Agarwal, Shivani Agarwal, Sepehr Assadi, and Sanjeev Khanna. Learning with limited rounds of adaptivity: Coin tossing, multi-armed bandits, and ranking from pairwise comparisons. In Conference on Learning Theory, pages 39–75. PMLR, 2017. [ACK18] Jayadev Acharya, Cl´ement L Canonne, and Gautam Kamath. A chasm between identity and equivalence testing with conditional queries. Theory of Computing, 14(19):1–46, 2018. [BC18] Rishiraj Bhattacharyya and Sourav Chakraborty. Property testing of joint distributions using conditional samples. ACM Transactions on Computation Theory (TOCT), 10(4):1–20, 2018. [BFR+13] Tu˘gkan Batu, Lance Fortnow, Ronitt Rubinfeld, Warren D Smith, and Patrick White. Testing closeness of discrete distributions. Journal of the ACM (JACM), 60(1):1–25, 2013. [BS18] Eric Balkanski and Yaron Singer. The adaptive complexity of maximizing a submodular function. In Proceedings of the 50th annual ACM SIGACT symposium on theory of computing, pages 1138– 1151, 2018. [CCK+21] Cl´ement L Canonne, Xi Chen, Gautam Kamath, Amit Levi, and Erik Waingarten. Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). SIAM, 2021. [CCK24] Diptarka Chakraborty, Sourav Chakraborty, and Gunjan Kumar. Tight lower bound on equivalence testing in conditional sampling model. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 4371–4394. SIAM, 2024. [CDVV14] Siu-On Chan, Ilias Diakonikolas, Paul Valiant, and Gregory Valiant. Optimal algorithms for testing closeness of discrete distributions. In Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms, pages 1193–1203. SIAM, 2014. [CFGM13] Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, and Arie Matsliah. On the power of conditional samples in distribution testing. In Proceedings of the 4th conference on Innovations in Theoretical Computer Science, pages 561–580, 2013. [CG18] Cl´ement L Canonne and Tom Gur. An adaptivity hierarchy theorem for property testing. computational complexity, 27:671–716, 2018. [CJLW21] Xi Chen, Rajesh Jayaram, Amit Levi, and Erik Waingarten. Learning and testing junta distributions with sub cube conditioning. In Conference on Learning Theory, pages 1060–1113. PMLR, 2021. [CKM23] Diptarka Chakraborty, Gunjan Kumar, and Kuldeep S. Meel. Support size estimation: The power of conditioning. In Proceedings of the 48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023, August 28 - September 01, 2023, 2023. [CM19] Sourav Chakraborty and Kuldeep S Meel. On testing of uniform samplers. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33-01, pages 7777–7784, 2019. [CQ19] Chandra Chekuri and Kent Quanrud. Parallelizing greedy for submodular set function maximization in matroids and beyond. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pages 78–89, 2019. [CRS14] Cl´ement Canonne, Dana Ron, and Rocco A Servedio. Testing equivalence between distributions using conditional samples. In Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms, pages 1174–1192. SIAM, 2014. [DHH00] Dingzhu Du, Frank K Hwang, and Frank Hwang. Combinatorial group testing and its applications, volume 12. World Scientific, 2000. [DMT13] Peter Damaschke, Azam Sheikh Muhammad, and Eberhard Triesch. Two new perspectives on multi-stage group testing. Algorithmica, 67:324–354, 2013. [EBE20] Jens Niklas Eberhardt, Nikolas Peter Breuckmann, and Christiane Sigrid Eberhardt. Multi-stage group testing improves efficiency of large-scale covid-19 screening. Journal of Clinical Virology, 128:104382, 2020. [FJO+15] Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapati, and Ananda Theertha Suresh. Faster algorithms for testing under conditional sampling. In Conference on Learning Theory, pages 607–636. PMLR, 2015. [GGR98] Oded Goldreich, Shari Goldwasser, and Dana Ron. Property testing and its connection to learning and approximation. Journal of the ACM (JACM), 45(4):653–750, 1998. [GJM22] Priyanka Golia, Brendan Juba, and Kuldeep S Meel. A scalable Shannon entropy estimator. In Computer Aided Verification: 34th International Conference, CAV 2022, Haifa, Israel, August 7–10, 2022, Proceedings, Part I, pages 363–384. Springer, 2022. [GR11] Oded Goldreich and Dana Ron. On testing expansion in bounded-degree graphs. Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation: In Collaboration with Lidor Avigad, Mihir Bellare, Zvika Brakerski, Shafi Goldwasser, Shai Halevi, Tali Kaufman, Leonid Levin, Noam Nisan, Dana Ron, Madhu Sudan, Luca Trevisan, Salil Vadhan, Avi Wigderson, David Zuckerman, pages 68–75, 2011. [KP19] Akshay Kamath and Eric Price. Adaptive sparse recovery with limited adaptivity. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2729–2744. SIAM, 2019. [KT19] Gautam Kamath and Christos Tzamos. Anaconda: A non-adaptive conditional sampling algorithm for distribution testing. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 679–693. SIAM, 2019. [MPC20] Kuldeep S Meel, Yash Pralhad Pote, and Sourav Chakraborty. On testing of samplers. Advances in Neural Information Processing Systems, 33:5753–5763, 2020. [Nar21] Shyam Narayanan. On tolerant distribution testing in the conditional sampling model. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 357– 373. SIAM, 2021. [NSWZ18] Vasileios Nakos, Xiaofei Shi, David P Woodruff, and Hongyang Zhang. Improved algorithms for adaptive compressed sensing. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. [Val11] Paul Valiant. Testing symmetric properties of distributions. SIAM Journal on Computing, 40(6):1927–1968, 2011. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Diptarka Chakraborty, National University of Singapore, Singapore (2) Sourav Chakraborty, Indian Statistical Institute, Kolkata; (3) Gunjan Kumar, National University of Singapore, Singapore; (4) Kuldeep S. Meel, University of Toronto, Toronto. Authors: Authors: (1) Diptarka Chakraborty, National University of Singapore, Singapore (2) Sourav Chakraborty, Indian Statistical Institute, Kolkata; (3) Gunjan Kumar, National University of Singapore, Singapore; (4) Kuldeep S. Meel, University of Toronto, Toronto. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Notations and Preliminaries 2 Notations and Preliminaries 3 Related Work 3 Related Work 4 An Efficient One-Round Adaptive Algorithm and 4.1 High-Level Overview 4 An Efficient One-Round Adaptive Algorithm and 4.1 High-Level Overview 4.2 Algorithm Description 4.2 Algorithm Description 4.3 Technical Analysis 4.3 Technical Analysis 5 Conclusion 5 Conclusion 6 Acknowledgements and References 6 Acknowledgements and References A Missing Proofs A Missing Proofs B An O(log log n)-query fully adaptive algorithm B An O(log log n)-query fully adaptive algorithm 6 Acknowledgements We thank the anonymous reviewers for their useful comments. D. Chakraborty is supported in part by an MoE AcRF Tier 2 grant (MOE-T2EP20221-0009), an MoE AcRF Tier 1 grant (T1 251RES2303), and a Google South & South-East Asia Research Award. K. S. Meel is supported in part by National Research Foundation Singapore under its NRF Fellowship Programme [NRF-NRFFAI1-2019-0004 ], Ministry of Education Singapore Tier 2 grant MOE-T2EP20121-0011, and Ministry of Education Singapore Tier 1 Grant [R-252-000-B59-114]. References [AAAK17] Arpit Agarwal, Shivani Agarwal, Sepehr Assadi, and Sanjeev Khanna. Learning with limited rounds of adaptivity: Coin tossing, multi-armed bandits, and ranking from pairwise comparisons. In Conference on Learning Theory, pages 39–75. PMLR, 2017. [ACK18] Jayadev Acharya, Cl´ement L Canonne, and Gautam Kamath. A chasm between identity and equivalence testing with conditional queries. Theory of Computing, 14(19):1–46, 2018. [BC18] Rishiraj Bhattacharyya and Sourav Chakraborty. Property testing of joint distributions using conditional samples. ACM Transactions on Computation Theory (TOCT), 10(4):1–20, 2018. [BFR+13] Tu˘gkan Batu, Lance Fortnow, Ronitt Rubinfeld, Warren D Smith, and Patrick White. Testing closeness of discrete distributions. Journal of the ACM (JACM), 60(1):1–25, 2013. [BS18] Eric Balkanski and Yaron Singer. The adaptive complexity of maximizing a submodular function. In Proceedings of the 50th annual ACM SIGACT symposium on theory of computing, pages 1138– 1151, 2018. [CCK+21] Cl´ement L Canonne, Xi Chen, Gautam Kamath, Amit Levi, and Erik Waingarten. Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). SIAM, 2021. [CCK24] Diptarka Chakraborty, Sourav Chakraborty, and Gunjan Kumar. Tight lower bound on equivalence testing in conditional sampling model. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 4371–4394. SIAM, 2024. [CDVV14] Siu-On Chan, Ilias Diakonikolas, Paul Valiant, and Gregory Valiant. Optimal algorithms for testing closeness of discrete distributions. In Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms, pages 1193–1203. SIAM, 2014. [CFGM13] Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, and Arie Matsliah. On the power of conditional samples in distribution testing. In Proceedings of the 4th conference on Innovations in Theoretical Computer Science, pages 561–580, 2013. [CG18] Cl´ement L Canonne and Tom Gur. An adaptivity hierarchy theorem for property testing. computational complexity, 27:671–716, 2018. [CJLW21] Xi Chen, Rajesh Jayaram, Amit Levi, and Erik Waingarten. Learning and testing junta distributions with sub cube conditioning. In Conference on Learning Theory, pages 1060–1113. PMLR, 2021. [CKM23] Diptarka Chakraborty, Gunjan Kumar, and Kuldeep S. Meel. Support size estimation: The power of conditioning. In Proceedings of the 48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023, August 28 - September 01, 2023, 2023. [CM19] Sourav Chakraborty and Kuldeep S Meel. On testing of uniform samplers. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33-01, pages 7777–7784, 2019. [CQ19] Chandra Chekuri and Kent Quanrud. Parallelizing greedy for submodular set function maximization in matroids and beyond. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pages 78–89, 2019. [CRS14] Cl´ement Canonne, Dana Ron, and Rocco A Servedio. Testing equivalence between distributions using conditional samples. In Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms, pages 1174–1192. SIAM, 2014. [DHH00] Dingzhu Du, Frank K Hwang, and Frank Hwang. Combinatorial group testing and its applications, volume 12. World Scientific, 2000. [DMT13] Peter Damaschke, Azam Sheikh Muhammad, and Eberhard Triesch. Two new perspectives on multi-stage group testing. Algorithmica, 67:324–354, 2013. [EBE20] Jens Niklas Eberhardt, Nikolas Peter Breuckmann, and Christiane Sigrid Eberhardt. Multi-stage group testing improves efficiency of large-scale covid-19 screening. Journal of Clinical Virology, 128:104382, 2020. [FJO+15] Moein Falahatgar, Ashkan Jafarpour, Alon Orlitsky, Venkatadheeraj Pichapati, and Ananda Theertha Suresh. Faster algorithms for testing under conditional sampling. In Conference on Learning Theory, pages 607–636. PMLR, 2015. [GGR98] Oded Goldreich, Shari Goldwasser, and Dana Ron. Property testing and its connection to learning and approximation. Journal of the ACM (JACM), 45(4):653–750, 1998. [GJM22] Priyanka Golia, Brendan Juba, and Kuldeep S Meel. A scalable Shannon entropy estimator. In Computer Aided Verification: 34th International Conference, CAV 2022, Haifa, Israel, August 7–10, 2022, Proceedings, Part I, pages 363–384. Springer, 2022. [GR11] Oded Goldreich and Dana Ron. On testing expansion in bounded-degree graphs. Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation: In Collaboration with Lidor Avigad, Mihir Bellare, Zvika Brakerski, Shafi Goldwasser, Shai Halevi, Tali Kaufman, Leonid Levin, Noam Nisan, Dana Ron, Madhu Sudan, Luca Trevisan, Salil Vadhan, Avi Wigderson, David Zuckerman, pages 68–75, 2011. [KP19] Akshay Kamath and Eric Price. Adaptive sparse recovery with limited adaptivity. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2729–2744. SIAM, 2019. [KT19] Gautam Kamath and Christos Tzamos. Anaconda: A non-adaptive conditional sampling algorithm for distribution testing. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 679–693. SIAM, 2019. [MPC20] Kuldeep S Meel, Yash Pralhad Pote, and Sourav Chakraborty. On testing of samplers. Advances in Neural Information Processing Systems, 33:5753–5763, 2020. [Nar21] Shyam Narayanan. On tolerant distribution testing in the conditional sampling model. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 357– 373. SIAM, 2021. [NSWZ18] Vasileios Nakos, Xiaofei Shi, David P Woodruff, and Hongyang Zhang. Improved algorithms for adaptive compressed sensing. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. [Val11] Paul Valiant. Testing symmetric properties of distributions. SIAM Journal on Computing, 40(6):1927–1968, 2011. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Equivalence Testing: The Power of Bounded Adaptivity: Acknowledgements and References

Authors:
(1) Florian Cafiero (ORCID 0000-0002-1951-6942), Sciences Po, Medialab;
(2) Jean-Baptiste Camps (ORCID 0000-0003-0385-7037), Ecole nationale des chartes, Universite Paris, Sciences & Lettres. Table of Links Abstract and Introduction Why work on QAnon? Specificities and social impact Who is Q? The theories put to test Authorship attribution Results Discussion Corpus constitution Quotes of authors outside of the corpus have been Definition of two subcorpus: dealing with generic difference and an imbalanced dataset The genre of “Q drops”: a methodological challenge Detecting style changes: rolling stylometry Ethical statement, Acknowledgements, and References Corpus constitution Because of their contested contents, many accounts have been deleted by the social media platforms. Other accounts were simply deleted by the user themselves. This raised many challenges for the corpus constitution, which had to rely on data collection realized before the deletion, or on difficulty searchable web archives. Moreover, all sources do not have the same time-span, and were created at different dates, discussing potentially different news, a source of heterogeneity in training material that creates challenge in the attribution procedure. We list here the sources we used for each candidate: Roger S We collected Roger S.’s posts on Gab (https://gab.com/RogerJStoneJr), from June 14th to August 2nd, 2021. Michael F Michael F. wrote a series of 10 articles for the Western Journal, from June 29, 2020 to July 31, 2021. (https://www.westernjournal.com/author/mflynn/). He also wrote a letter to ask for support to Roger S.’s wife, published on FrankReport (https://frankreport.com/2021/06/11/bannedby-twitter-gen-michael-flynn-is-published-on-frankreport-concerning-roger-stone/). His article for Fox News about ISIS has also been analyzed. (https://web.archive.org/web- /20161215042531/http://www.foxnews.com/opinion/2016/11/02/gen-michaelflynn-after-mosul-is-liberated-isis-could-attack-usnext.html). Finally, we collected posts on his Twitter account from October 19th, 2016 to September 18th, 2017. Paul F We collected Paul F.’s personal writing on his website (https://paulfurber.net/). We retrieved archives from his twitter on account of a threadreader (https://threadreaderapp.- com/thread/1158540523008905216.html). We also captured archives from the CBTS boards on 8chan, where he wrote as “The Board Owner”. A few posts he left on Discord were transcribed from pictures found online. Finally, Paul F. wrote a book: Q: Inside The Greatest Intelligence Drop In History, included in our large corpus. Jim W Archives of Jim W.’s Twitter account were found on archive.today (https://archive.is- /https://twitter.com/xerxeswatkins), which preserves 9 screenshots (22 Dec 2014, 6 Feb 2016, 15 Mar 2016, 30 Mar 2016, 4 Apr 2016, 5 May 2016, 28 May 2016, 25 Mar 2017, 8 Apr 2017) taken prior to the account suspension. A large amount of these tweets were only citing article titles from his own media The Goldwater. As these titles were not necessarily (and probably not) written by him, we chose to exclude them. A small text was written by Jim W. on 5ch about a service problem on 8ch that he blames on a government attack. (https://fox.5ch.net/test/read.cgi/poverty/1418- 027836/826) Finally, posts from his Parler account were added to the corpus. Ron W A sample of 3130 tweets by Ron W. have been collected through the Twitter API. We also collected his posts on Telegram from November 30th, 2021 to December, 20th, 2021. Coleman R Under the pseudonym PamphletAnon, Coleman R. wrote a vast number of posts on 8chan, especially on the board “the Storm” (https://8ch.net/thestorm/catalog.html) of which he was the owner. We collected his posts on the Wayback Machine, which seems to provide a complete archive of the board. A few messages he posted on Discord (Q Central, 2017) have been archived by DDOS (https://ddosecrets.com/wiki/Distributed Denial of Secrets), at this address https://whispers.ddosecrets.com/discord/user/376607495470448643. 347 messages by PamphletAnon on Discord (Patriots’ Soapbox, 2018) are also available at: https://discordleaks.unicornriot.ninja/discord/user/41936. We also found a small text on Reddit, where Coleman R. announces a future talk on Infowars with Rob Dew. On September 11, 2020, Pamphlet Anon wrote a text on “Patriots’ Soapbox”, the media he curates with Christina U. (https://patriotssoapbox.com/opinion/memories-of9-11-surreal-and-terrifying/). Courtney T Collaborating with Ron and Jim W., Courtney T. publicly announced that she knew the truth about the Q drops, and that it would be highly disappointing to their public (Huback, 2021). We collected her posts on Twitter, under her account IWillRedPillYou, archived here (http://web.archive.org/web/20180113162029if /-https://twitter.com/IWillRedPillYou). Tracy D Under the pseudonym Tracy Beanz, Tracy D. published a large number of tweets, on an account now suspended, but of which archives.today retains 92 captures (https://archive.vn/lDRyR), from December 2016 to January 2021. She also published a long post explaining herself about quarrels over Q related publications on Steemit (https://steemit.com/drama/@tracybeanz/shestood-in-the-storm) Christina U Christina U. wrote a number of articles on PatriotsSoapbox (https://patriotssoapbox.com/), of which the 5 most recent on July 7h, 2021 were collected. We also found an online conversation she had on Muckrock with Homeland Security on the 7th and 22nd of July 2021. (https://www.muckrock.com/foi/united-statesof-america-10/patriots-soapbox-department-ofhomeland-security-115196/#file-956999) Archives of her GAB profile were also analyzed. Donald T Former president of the United States tweets were collected during the month of december 2020. We removed tweets suspected to have been written by his staff by the site https://factba.se/. Melania T We collected a sample of tweets by former FLOTUS thanks to the Twitter API, from January 21st, 2017 to January 19th, 2021. Eric T We collected a sample of 3000 tweets by the son of former POTUS thanks to the Twitter API from September 10th 2016, to June 24th 2021. Dan S We collected a sample of tweets by the former POTUS’ deputy chief of staff thanks to the Twitter API, from October 25th, 2018 to January 20th, 2021. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Florian Cafiero (ORCID 0000-0002-1951-6942), Sciences Po, Medialab; (2) Jean-Baptiste Camps (ORCID 0000-0003-0385-7037), Ecole nationale des chartes, Universite Paris, Sciences & Lettres. Authors: Authors: (1) Florian Cafiero (ORCID 0000-0002-1951-6942), Sciences Po, Medialab; (2) Jean-Baptiste Camps (ORCID 0000-0003-0385-7037), Ecole nationale des chartes, Universite Paris, Sciences & Lettres. Table of Links Abstract and Introduction Abstract and Introduction Why work on QAnon? Specificities and social impact Why work on QAnon? Specificities and social impact Who is Q? The theories put to test Who is Q? The theories put to test Authorship attribution Authorship attribution Results Results Discussion Discussion Corpus constitution Corpus constitution Quotes of authors outside of the corpus have been Quotes of authors outside of the corpus have been Definition of two subcorpus: dealing with generic difference and an imbalanced dataset Definition of two subcorpus: dealing with generic difference and an imbalanced dataset The genre of “Q drops”: a methodological challenge The genre of “Q drops”: a methodological challenge Detecting style changes: rolling stylometry Detecting style changes: rolling stylometry Ethical statement, Acknowledgements, and References Ethical statement, Acknowledgements, and References Corpus constitution Because of their contested contents, many accounts have been deleted by the social media platforms. Other accounts were simply deleted by the user themselves. This raised many challenges for the corpus constitution, which had to rely on data collection realized before the deletion, or on difficulty searchable web archives. Moreover, all sources do not have the same time-span, and were created at different dates, discussing potentially different news, a source of heterogeneity in training material that creates challenge in the attribution procedure. We list here the sources we used for each candidate: Roger S We collected Roger S.’s posts on Gab (https://gab.com/RogerJStoneJr), from June 14th to August 2nd, 2021. Roger S Michael F Michael F. wrote a series of 10 articles for the Western Journal, from June 29, 2020 to July 31, 2021. (https://www.westernjournal.com/author/mflynn/). He also wrote a letter to ask for support to Roger S.’s wife, published on FrankReport (https://frankreport.com/2021/06/11/bannedby-twitter-gen-michael-flynn-is-published-on-frankreport-concerning-roger-stone/). Michael F His article for Fox News about ISIS has also been analyzed. (https://web.archive.org/web- /20161215042531/http://www.foxnews.com/opinion/2016/11/02/gen-michaelflynn-after-mosul-is-liberated-isis-could-attack-usnext.html). Finally, we collected posts on his Twitter account from October 19th, 2016 to September 18th, 2017. Paul F We collected Paul F.’s personal writing on his website (https://paulfurber.net/). Paul F We retrieved archives from his twitter on account of a threadreader (https://threadreaderapp.- com/thread/1158540523008905216.html). We also captured archives from the CBTS boards on 8chan, where he wrote as “The Board Owner”. A few posts he left on Discord were transcribed from pictures found online. Finally, Paul F. wrote a book: Q: Inside The Greatest Intelligence Drop In History, included in our large corpus. Jim W Archives of Jim W.’s Twitter account were found on archive.today (https://archive.is- /https://twitter.com/xerxeswatkins), which preserves 9 screenshots (22 Dec 2014, 6 Feb 2016, 15 Mar 2016, 30 Mar 2016, 4 Apr 2016, 5 May 2016, 28 May 2016, 25 Mar 2017, 8 Apr 2017) taken prior to the account suspension. A large amount of these tweets were only citing article titles from his own media The Goldwater. As these titles were not necessarily (and probably not) written by him, we chose to exclude them. Jim W A small text was written by Jim W. on 5ch about a service problem on 8ch that he blames on a government attack. (https://fox.5ch.net/test/read.cgi/poverty/1418- 027836/826) Finally, posts from his Parler account were added to the corpus. Ron W A sample of 3130 tweets by Ron W. have been collected through the Twitter API. Ron W We also collected his posts on Telegram from November 30th, 2021 to December, 20th, 2021. Coleman R Under the pseudonym PamphletAnon, Coleman R. wrote a vast number of posts on 8chan, especially on the board “the Storm” (https://8ch.net/thestorm/catalog.html) of which he was the owner. We collected his posts on the Wayback Machine, which seems to provide a complete archive of the board. Coleman R A few messages he posted on Discord (Q Central, 2017) have been archived by DDOS (https://ddosecrets.com/wiki/Distributed Denial of Secrets), at this address https://whispers.ddosecrets.com/discord/user/376607495470448643. 347 messages by PamphletAnon on Discord (Patriots’ Soapbox, 2018) are also available at: https://discordleaks.unicornriot.ninja/discord/user/41936. We also found a small text on Reddit, where Coleman R. announces a future talk on Infowars with Rob Dew. On September 11, 2020, Pamphlet Anon wrote a text on “Patriots’ Soapbox”, the media he curates with Christina U. (https://patriotssoapbox.com/opinion/memories-of9-11-surreal-and-terrifying/). Courtney T Collaborating with Ron and Jim W., Courtney T. publicly announced that she knew the truth about the Q drops, and that it would be highly disappointing to their public (Huback, 2021). We collected her posts on Twitter, under her account IWillRedPillYou, archived here (http://web.archive.org/web/20180113162029if /- https://twitter.com/IWillRedPillYou). Courtney T https://twitter.com/IWillRedPillYou). Tracy D Under the pseudonym Tracy Beanz, Tracy D. published a large number of tweets, on an account now suspended, but of which archives.today retains 92 captures (https://archive.vn/lDRyR), from December 2016 to January 2021. Tracy D She also published a long post explaining herself about quarrels over Q related publications on Steemit (https://steemit.com/drama/@tracybeanz/shestood-in-the-storm) Christina U Christina U. wrote a number of articles on PatriotsSoapbox (https://patriotssoapbox.com/), of which the 5 most recent on July 7h, 2021 were collected. Christina U We also found an online conversation she had on Muckrock with Homeland Security on the 7th and 22nd of July 2021. (https://www.muckrock.com/foi/united-statesof-america-10/patriots-soapbox-department-ofhomeland-security-115196/#file-956999) Archives of her GAB profile were also analyzed. Donald T Former president of the United States tweets were collected during the month of december 2020. We removed tweets suspected to have been written by his staff by the site https://factba.se/. Donald T Melania T We collected a sample of tweets by former FLOTUS thanks to the Twitter API, from January 21st, 2017 to January 19th, 2021. Melania T Eric T We collected a sample of 3000 tweets by the son of former POTUS thanks to the Twitter API from September 10th 2016, to June 24th 2021. Eric T Dan S We collected a sample of tweets by the former POTUS’ deputy chief of staff thanks to the Twitter API, from October 25th, 2018 to January 20th, 2021. Dan S This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Challenges in Building a QAnon Authorship Corpus

Everything You Need to Know About Zero-Knowledge Proof (ZKP) Technology

How Decentralized Interaction Protocols Work: Analyzing VC, ZKP, and Āut’s Interaction Tree

Authors:
(1) Seokil Ham, KAIST;
(2) Jungwuk Park, KAIST;
(3) Dong-Jun Han, Purdue University;
(4) Jaekyun Moon, KAIST. Table of Links Abstract and 1. Introduction 2. Related Works 3. Proposed NEO-KD Algorithm and 3.1 Problem Setup: Adversarial Training in Multi-Exit Networks 3.2 Algorithm Description 4. Experiments and 4.1 Experimental Setup 4.2. Main Experimental Results 4.3. Ablation Studies and Discussions 5. Conclusion, Acknowledgement and References A. Experiment Details B. Clean Test Accuracy and C. Adversarial Training via Average Attack D. Hyperparameter Tuning E. Discussions on Performance Degradation at Later Exits F. Comparison with Recent Defense Methods for Single-Exit Networks G. Comparison with SKD and ARD and H. Implementations of Stronger Attacker Algorithms 5 Conclusion In this paper, we proposed a new knowledge distillation based adversarial training strategy for robust multi-exit networks. Our solution, NEO-KD, reduces adversarial transferability in the network while guiding the output of the adversarial examples to closely follow the ensemble outputs of the neighbor exits of the clean data, significantly improving the overall adversarial test accuracy. Extensive experimental results on both anytime and budgeted prediction setups using various datasets confirmed the effectiveness of our method, compared to baselines relying on existing adversarial training or knowledge distillation techniques for multi-exit networks. Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1I1A2A02061135), by the Center for Applied Research in Artificial Intelligence (CARAI) grant funded by DAPA and ADD (UD230017TD), and by IITP funds from MSIT of Korea (No. 2020-0-00626). References [1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In Computer Vision– ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XXIII, pages 484–501. Springer, 2020. [2] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017 ieee symposium on security and privacy (sp), pages 39–57. Ieee, 2017. [3] Sihong Chen, Haojing Shen, Ran Wang, and Xizhao Wang. Towards improving fast adversarial training in multi-exit network. Neural Networks, 150:1–11, 2022. [4] Francesco Croce and Matthias Hein. Minimally distorted adversarial examples with a fast adaptive boundary attack. In International Conference on Machine Learning, pages 2196–2205. PMLR, 2020. [5] Francesco Croce and Matthias Hein. Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks. In International conference on machine learning, pages 2206–2216. PMLR, 2020. [6] Junhao Dong, Seyed-Mohsen Moosavi-Dezfooli, Jianhuang Lai, and Xiaohua Xie. The enemy of my enemy is my friend: Exploring inverse adversaries for improving adversarial training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 24678–24687, 2023. [7] Yinpeng Dong, Ke Xu, Xiao Yang, Tianyu Pang, Zhijie Deng, Hang Su, and Jun Zhu. Exploring memorization in adversarial training. arXiv preprint arXiv:2106.01606, 2021. [8] Micah Goldblum, Liam Fowl, Soheil Feizi, and Tom Goldstein. Adversarially robust distillation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 3996–4003, 2020. [9] Dong-Jun Han, Jungwuk Park, Seokil Ham, Namjin Lee, and Jaekyun Moon. Improving lowlatency predictions in multi-exit neural networks via block-dependent losses. IEEE Transactions on Neural Networks and Learning Systems, 2023. [10] Mirazul Haque, Anki Chauhan, Cong Liu, and Wei Yang. Ilfo: Adversarial attack on adaptive neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14264–14273, 2020. [11] Sanghyun Hong, Yigitcan Kaya, Ionut,-Vlad Modoranu, and Tudor Dumitras. A panda? no, it’s a sloth: Slowdown attacks on adaptive multi-exit neural network inference. In International Conference on Learning Representations, 2020. [12] Ting-Kuei Hu, Tianlong Chen, Haotao Wang, and Zhangyang Wang. Triple wins: Boosting accuracy, robustness and efficiency together by enabling input-adaptive inference. In International Conference on Learning Representations, 2020. [13] Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens Van Der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. arXiv preprint arXiv:1703.09844, 2017. [14] Hoki Kim. Torchattacks: A pytorch repository for adversarial attacks. arXiv preprint arXiv:2010.01950, 2020. [15] Alexandros Kouris, Stylianos I Venieris, Stefanos Laskaridis, and Nicholas Lane. Multi-exit semantic segmentation networks. In European Conference on Computer Vision, pages 330–349. Springer, 2022. [16] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009. [17] Ya Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 231N, 7(7):3, 2015. [18] Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998. [19] Sungyoon Lee, Hoki Kim, and Jaewook Lee. Graddiv: Adversarial robustness of randomized neural networks via gradient diversity regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. [20] Hao Li, Hong Zhang, Xiaojuan Qi, Ruigang Yang, and Gao Huang. Improved techniques for training adaptive deep networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1891–1900, 2019. [21] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks. In International Conference on Learning Representations, 2018. [22] Tianyu Pang, Kun Xu, Chao Du, Ning Chen, and Jun Zhu. Improving adversarial robustness via promoting ensemble diversity. In International Conference on Machine Learning, pages 4970–4979. PMLR, 2019. [23] Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami. Distillation as a defense to adversarial perturbations against deep neural networks. In 2016 IEEE symposium on security and privacy (SP), pages 582–597. IEEE, 2016. [24] Mary Phuong and Christoph H Lampert. Distillation-based training for multi-exit architectures. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1355– 1364, 2019. [25] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. International journal of computer vision, 115:211–252, 2015. [26] Surat Teerapittayanon, Bradley McDanel, and Hsiang-Tsung Kung. Branchynet: Fast inference via early exiting from deep neural networks. In 2016 23rd International Conference on Pattern Recognition (ICPR), pages 2464–2469. IEEE, 2016. [27] Xinglu Wang and Yingming Li. Harmonized dense knowledge distillation training for multi-exit architectures. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 10218–10226, 2021. [28] Qunliang Xing, Mai Xu, Tianyi Li, and Zhenyu Guan. Early exit or not: Resource-efficient blind quality enhancement for compressed images. In European Conference on Computer Vision, pages 275–292. Springer, 2020. [29] Huanrui Yang, Jingyang Zhang, Hongliang Dong, Nathan Inkawhich, Andrew Gardner, Andrew Touchet, Wesley Wilkes, Heath Berry, and Hai Li. Dverge: diversifying vulnerabilities for enhanced robust generation of ensembles. Advances in Neural Information Processing Systems, 33:5505–5515, 2020. [30] Zhuolin Yang, Linyi Li, Xiaojun Xu, Shiliang Zuo, Qian Chen, Pan Zhou, Benjamin Rubinstein, Ce Zhang, and Bo Li. Trs: Transferability reduced ensemble via promoting gradient diversity and model smoothness. Advances in Neural Information Processing Systems, 34, 2021. [31] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan. Theoretically principled trade-off between robustness and accuracy. In International conference on machine learning, pages 7472–7482. PMLR, 2019. [32] Wangchunshu Zhou, Canwen Xu, Tao Ge, Julian McAuley, Ke Xu, and Furu Wei. Bert loses patience: Fast and robust inference with early exit. Advances in Neural Information Processing Systems, 33:18330–18341, 2020. [33] Jianing Zhu, Jiangchao Yao, Bo Han, Jingfeng Zhang, Tongliang Liu, Gang Niu, Jingren Zhou, Jianliang Xu, and Hongxia Yang. Reliable adversarial distillation with unreliable teachers. arXiv preprint arXiv:2106.04928, 2021. [34] Bojia Zi, Shihao Zhao, Xingjun Ma, and Yu-Gang Jiang. Revisiting adversarial robustness distillation: Robust soft labels make student better. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 16443–16452, 2021. This paper is available on arxiv under CC 4.0 license. Authors: (1) Seokil Ham, KAIST; (2) Jungwuk Park, KAIST; (3) Dong-Jun Han, Purdue University; (4) Jaekyun Moon, KAIST. Authors: Authors: (1) Seokil Ham, KAIST; (2) Jungwuk Park, KAIST; (3) Dong-Jun Han, Purdue University; (4) Jaekyun Moon, KAIST. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Related Works 2. Related Works 3. Proposed NEO-KD Algorithm and 3.1 Problem Setup: Adversarial Training in Multi-Exit Networks 3. Proposed NEO-KD Algorithm and 3.1 Problem Setup: Adversarial Training in Multi-Exit Networks 3.2 Algorithm Description 3.2 Algorithm Description 4. Experiments and 4.1 Experimental Setup 4. Experiments and 4.1 Experimental Setup 4.2. Main Experimental Results 4.2. Main Experimental Results 4.3. Ablation Studies and Discussions 4.3. Ablation Studies and Discussions 5. Conclusion, Acknowledgement and References 5. Conclusion, Acknowledgement and References A. Experiment Details A. Experiment Details B. Clean Test Accuracy and C. Adversarial Training via Average Attack B. Clean Test Accuracy and C. Adversarial Training via Average Attack D. Hyperparameter Tuning D. Hyperparameter Tuning E. Discussions on Performance Degradation at Later Exits E. Discussions on Performance Degradation at Later Exits F. Comparison with Recent Defense Methods for Single-Exit Networks F. Comparison with Recent Defense Methods for Single-Exit Networks G. Comparison with SKD and ARD and H. Implementations of Stronger Attacker Algorithms G. Comparison with SKD and ARD and H. Implementations of Stronger Attacker Algorithms 5 Conclusion In this paper, we proposed a new knowledge distillation based adversarial training strategy for robust multi-exit networks. Our solution, NEO-KD, reduces adversarial transferability in the network while guiding the output of the adversarial examples to closely follow the ensemble outputs of the neighbor exits of the clean data, significantly improving the overall adversarial test accuracy. Extensive experimental results on both anytime and budgeted prediction setups using various datasets confirmed the effectiveness of our method, compared to baselines relying on existing adversarial training or knowledge distillation techniques for multi-exit networks. Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1I1A2A02061135), by the Center for Applied Research in Artificial Intelligence (CARAI) grant funded by DAPA and ADD (UD230017TD), and by IITP funds from MSIT of Korea (No. 2020-0-00626). References [1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In Computer Vision– ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XXIII, pages 484–501. Springer, 2020. [2] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017 ieee symposium on security and privacy (sp), pages 39–57. Ieee, 2017. [3] Sihong Chen, Haojing Shen, Ran Wang, and Xizhao Wang. Towards improving fast adversarial training in multi-exit network. Neural Networks, 150:1–11, 2022. [4] Francesco Croce and Matthias Hein. Minimally distorted adversarial examples with a fast adaptive boundary attack. In International Conference on Machine Learning, pages 2196–2205. PMLR, 2020. [5] Francesco Croce and Matthias Hein. Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks. In International conference on machine learning, pages 2206–2216. PMLR, 2020. [6] Junhao Dong, Seyed-Mohsen Moosavi-Dezfooli, Jianhuang Lai, and Xiaohua Xie. The enemy of my enemy is my friend: Exploring inverse adversaries for improving adversarial training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 24678–24687, 2023. [7] Yinpeng Dong, Ke Xu, Xiao Yang, Tianyu Pang, Zhijie Deng, Hang Su, and Jun Zhu. Exploring memorization in adversarial training. arXiv preprint arXiv:2106.01606, 2021. [8] Micah Goldblum, Liam Fowl, Soheil Feizi, and Tom Goldstein. Adversarially robust distillation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 3996–4003, 2020. [9] Dong-Jun Han, Jungwuk Park, Seokil Ham, Namjin Lee, and Jaekyun Moon. Improving lowlatency predictions in multi-exit neural networks via block-dependent losses. IEEE Transactions on Neural Networks and Learning Systems, 2023. [10] Mirazul Haque, Anki Chauhan, Cong Liu, and Wei Yang. Ilfo: Adversarial attack on adaptive neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14264–14273, 2020. [11] Sanghyun Hong, Yigitcan Kaya, Ionut,-Vlad Modoranu, and Tudor Dumitras. A panda? no, it’s a sloth: Slowdown attacks on adaptive multi-exit neural network inference. In International Conference on Learning Representations, 2020. [12] Ting-Kuei Hu, Tianlong Chen, Haotao Wang, and Zhangyang Wang. Triple wins: Boosting accuracy, robustness and efficiency together by enabling input-adaptive inference. In International Conference on Learning Representations, 2020. [13] Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens Van Der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. arXiv preprint arXiv:1703.09844, 2017. [14] Hoki Kim. Torchattacks: A pytorch repository for adversarial attacks. arXiv preprint arXiv:2010.01950, 2020. [15] Alexandros Kouris, Stylianos I Venieris, Stefanos Laskaridis, and Nicholas Lane. Multi-exit semantic segmentation networks. In European Conference on Computer Vision, pages 330–349. Springer, 2022. [16] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009. [17] Ya Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 231N, 7(7):3, 2015. [18] Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998. [19] Sungyoon Lee, Hoki Kim, and Jaewook Lee. Graddiv: Adversarial robustness of randomized neural networks via gradient diversity regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. [20] Hao Li, Hong Zhang, Xiaojuan Qi, Ruigang Yang, and Gao Huang. Improved techniques for training adaptive deep networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1891–1900, 2019. [21] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks. In International Conference on Learning Representations, 2018. [22] Tianyu Pang, Kun Xu, Chao Du, Ning Chen, and Jun Zhu. Improving adversarial robustness via promoting ensemble diversity. In International Conference on Machine Learning, pages 4970–4979. PMLR, 2019. [23] Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami. Distillation as a defense to adversarial perturbations against deep neural networks. In 2016 IEEE symposium on security and privacy (SP), pages 582–597. IEEE, 2016. [24] Mary Phuong and Christoph H Lampert. Distillation-based training for multi-exit architectures. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1355– 1364, 2019. [25] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. International journal of computer vision, 115:211–252, 2015. [26] Surat Teerapittayanon, Bradley McDanel, and Hsiang-Tsung Kung. Branchynet: Fast inference via early exiting from deep neural networks. In 2016 23rd International Conference on Pattern Recognition (ICPR), pages 2464–2469. IEEE, 2016. [27] Xinglu Wang and Yingming Li. Harmonized dense knowledge distillation training for multi-exit architectures. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 10218–10226, 2021. [28] Qunliang Xing, Mai Xu, Tianyi Li, and Zhenyu Guan. Early exit or not: Resource-efficient blind quality enhancement for compressed images. In European Conference on Computer Vision, pages 275–292. Springer, 2020. [29] Huanrui Yang, Jingyang Zhang, Hongliang Dong, Nathan Inkawhich, Andrew Gardner, Andrew Touchet, Wesley Wilkes, Heath Berry, and Hai Li. Dverge: diversifying vulnerabilities for enhanced robust generation of ensembles. Advances in Neural Information Processing Systems, 33:5505–5515, 2020. [30] Zhuolin Yang, Linyi Li, Xiaojun Xu, Shiliang Zuo, Qian Chen, Pan Zhou, Benjamin Rubinstein, Ce Zhang, and Bo Li. Trs: Transferability reduced ensemble via promoting gradient diversity and model smoothness. Advances in Neural Information Processing Systems, 34, 2021. [31] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan. Theoretically principled trade-off between robustness and accuracy. In International conference on machine learning, pages 7472–7482. PMLR, 2019. [32] Wangchunshu Zhou, Canwen Xu, Tao Ge, Julian McAuley, Ke Xu, and Furu Wei. Bert loses patience: Fast and robust inference with early exit. Advances in Neural Information Processing Systems, 33:18330–18341, 2020. [33] Jianing Zhu, Jiangchao Yao, Bo Han, Jingfeng Zhang, Tongliang Liu, Gang Niu, Jingren Zhou, Jianliang Xu, and Hongxia Yang. Reliable adversarial distillation with unreliable teachers. arXiv preprint arXiv:2106.04928, 2021. [34] Bojia Zi, Shihao Zhao, Xingjun Ma, and Yu-Gang Jiang. Revisiting adversarial robustness distillation: Robust soft labels make student better. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 16443–16452, 2021. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

How NEO-KD Reduces Adversarial Transferability and Improves Accuracy

Optimizing Prompts with LLMs: Key Findings and Future Directions

Authors:
(1) Taha Laroussi, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France;
(2) Mojtaba Jarrahi, Universit´e Paris-Saclay, CNRS, FAST, 91405 Orsay, France;
(3) Gabriel Amselem, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France. Table of Links Abstract and Introduction Methods Results Model Discussion, Acknowledgements and References Supplementary Material V. DISCUSSION We have shown experimentally that the change in phototactic behavior of C. reinhardtii can be due to its recent history of illumination. When exposed to two closely spaced, identical stimuli, the algae act as if they were time-integrating the stimuli. This is visible when the stimulus is close to that delimiting positive and negative phototaxis. Then, the algae show two different behaviors in response to the two consecutive stimuli: first a backand-forth response, then a negative phototaxis. When the stimuli are sufficiently spaced apart, the algae have had time to relax to a basal state, and show the same qualitative response to the two stimuli, see Fig. 6. In our experiments, we find this time of complete relaxation to be approximately equal to 30 minutes. A simplified model of phototaxis explains this memory effect by the introduction of a time-scale of relaxation in the inner biochemistry of the cell. When the time-scale of relaxation is larger than the time between two consecutive stimuli, the alga integrates the signal and can display different behaviors in response to the two identical stimuli, see Fig. 8. The time needed to return to the basal state should be of order 3τ , which underlies our choice of τ = 10 min for the relaxation time constant. Our experimental data are consistent with an inner relaxation time τ in the range ≈ 5 to 20 minutes. What could be the biochemical species corresponding to the intracellular species S introduced in the model? It is very likely that our simplified model compounds the dynamics of multiple biochemical species, activated sequentially in a signalling cascade. Still, it is known that the photoreceptors for phototaxis in C. reinhardtii are channelrhodopsins, that become phosphorylated within milliseconds after the application of a light stimulus. A high level of phosphorylated channelrhodopsin-1 (ChR1) in the cell correlates with a change from positive to negative phototaxis [11], much like a high level of activated S corresponds to negative phototaxis in our model. Moreover, the time scale of dephosphorylation of ChR1 in C. reinhardtii has been shown to be of the order of ≈ 5 to 15 minutes [11], which is compatible with our value of τ = 10 min. A possibility is therefore to identify S with ChR1. A more physical model of phototaxis was recently introduced by Leptos et al. to describe the response of C. reinhardtii to light [22]. In their model, Leptos et al. take into account the rotation of the microalga around its axis while swimming, and the resulting oscillating light intensity seen by the eyespot. The consecutive step-up and step-down stimuli sensed by the eyespot during one body rotation lead to a realignment of the trajectory towards the light source. Our model averages out the body rotation of the microalgae and describes the behavior of the microorganism at a more coarse-grained time-scale. Another difference is that the model of Leptos et al. does not take into account the fact that phototaxis changes sign when the light intensity increases. This change of phototactic behavior requires the introduction of a threshold value in the model, below (resp. above) which phototaxis is positive (resp. negative). Such a threshold is incorporated in our simplified model. Note that the threshold in the model, introduced as a simple means to obtain a change in behavior between positive and negative phototaxis at different light intensities, leads to the back-and-forth behavior at intermediate light intensities. The existence of this threshold also enables to explain why the time scale of negative phototaxis is longer than that of positive phototaxis. Negative phototaxis occurs when the amount of active species s ⋆ overcomes a threshold sT ; this takes time, during which the alga exhibits positive phototaxis. Only when s ⋆ > sT do the algae show negative phototaxis, and accumulate at one boundary of the well. The small initial positive phototactic response predicted by the model is in agreement with experimental data. The model also predicts that it is possible to switch the phototactic behavior of algae from positive phototaxis to back-and-forth to negative phototaxis, using three consecutive identical stimuli, by adjusting the waiting times between the stimuli and choosing carefully the stimulus intensity, see Fig. 8d. While we were not able to find the experimental conditions corresponding to this theoretical prediction, we were able to experimentally observe the switch from back-and-forth to negative phototaxis, and from positive phototaxis to back-and-forth in a couple experiments, see Supp. Fig. 5. While the model successfully reproduces the phototactic behavior and the time scales at play, it fails to reproduce two experimental observations. First, in a couple experiments, multiple consecutive back-and-forth of the center of mass were observed at intermediate intensities, see Supp. Fig. 6. Second, in experiments with consecutive stimuli at intermediate light intensities, algae in the third experiment (after a waiting time of 30 minutes) display positive phototaxis instead of the expected backand-forth behavior observed during the first experiment, see Fig. 6b and Supp. Fig. 5. Both behaviors can be obtained in the model by supposing that the threshold sT increases with the time spent under a light stimulus, and so depends on the history of the microorganism. Such an increasing threshold would also enable to recover the traditional adaptative behavior at longer time scales [15]. This implies having a third equation describing the timeevolution of sT , thus introducing another time constant into the problem. In the lab, the memory effects reported here imply that it is not possible to repeat the same phototaxis experiments on a given batch of cells and expect similar outcomes. Such an effect was already known in the case of long-term adaptation [15]. The data reported here show that even in the case of short-term experiments, the behavior is not necessarily reproducible. To study phototaxis quantitatively, experimental repeats should be carried out with different batches of naive cells. Having identified this short time-scale, our experiments pave the way for the study of phototaxis in the presence of timevarying light stimuli, much as the algae are subject to in their natural environment. There, light is constantly fluctuating. The short-term memory could then be a beneficial way to integrate a light signal randomly interrupted by the shadow of other motile organisms or objects. ACKNOWLEDGMENTS We thank David Gonzalez-Rodriguez for insightful comments on an early version of the model, Maxime Simon for preliminary experiments, Salome Guttierez Ramos for help with microfabrication, and Caroline Frot for precious technical support. This work was supported by “Investissements d’Avenir” LabEx PALM (ANR-10- LABX-0039-PALM) and by PEPS “M´ecanique du futur”. References [1] G. J´ekely, Philosophical Transactions of the Royal Society B: Biological Sciences 364, 2795 (2009). [2] K. W. Foster and R. D. Smyth, Microbiological reviews 44, 572 (1980). [3] P. Hegemann and P. Berthold, in The Chlamydomonas Sourcebook (Elsevier, 2009) pp. 395–429. [4] U. R¨uffer and W. Nultsch, Cell motility and the cytoskeleton 18, 269 (1991). [5] M. E. H. Feinleib and G. M. Curry, Physiologia Plantarum 25, 346 (1971). [6] W. Nultsch, J. Pfau, and R. Dolle, Archives of microbiology 144, 393 (1986). [7] N. Morel-Laurens, Photochemistry and Photobiology 45, 119 (1987). [8] R. Dolle, J. Pfau, and W. Nultsch, Journal of plant physiology 126, 467 (1987). [9] T. Takahashi and M. Watanabe, FEBS Letters 336, 516 (1993). [10] K.-i. Wakabayashi, Y. Misawa, S. Mochiji, and R. Kamiya, Proceedings of the National Academy of Sciences 108, 11280 (2011). [11] M. B¨ohm, D. Boness, E. Fantisch, H. Erhard, J. Frauenholz, Z. Kowalzyk, N. Marcinkowski, S. Kateriya, P. Hegemann, and G. Kreimer, The Plant Cell 31, 886 (2019). [12] R. M. Macnab and D. E. Koshland Jr, Proceedings of the National Academy of Sciences 69, 2509 (1972). [13] H. C. Berg and P. Tedesco, Proceedings of the National Academy of Sciences 72, 3235 (1975). [14] P. Van Haastert, The Journal of cell biology 96, 1559 (1983). [15] A. Mayer, Nature 217, 875 (1968). [16] E. Harris, D. Stern, and G. Witman, The chlamydomonas sourcebook, vol. 1 san diego (2009). [17] Y. Xia and G. M. Whitesides, Annual review of materials science 28, 153 (1998). [18] N. Ueki, T. Ide, S. Mochiji, Y. Kobayashi, R. Tokutsu, N. Ohnishi, K. Yamaguchi, S. Shigenobu, K. Tanaka, J. Minagawa, et al., Proceedings of the National Academy of Sciences 113, 5299 (2016). [19] A. Ramamonjy, J. Dervaux, and P. Brunet, Physical Review Letters 128, 258101 (2022). [20] C. T. Kreis, M. Le Blay, C. Linne, M. M. Makowski, and O. B¨aumchen, Nature Physics 14, 45 (2018). [21] S. Till, F. Ebmeier, A. A. Fragkopoulos, M. G. Mazza, and O. B¨aumchen, Physical Review Research 4, L042046 (2022). [22] K. C. Leptos, M. Chioccioli, S. Furlan, A. I. Pesci, and R. E. Goldstein, Physical Review E 107 (2023). This paper is available on arxiv under CC 4.0 license. Authors: (1) Taha Laroussi, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France; (2) Mojtaba Jarrahi, Universit´e Paris-Saclay, CNRS, FAST, 91405 Orsay, France; (3) Gabriel Amselem, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France. Authors: Authors: (1) Taha Laroussi, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France; (2) Mojtaba Jarrahi, Universit´e Paris-Saclay, CNRS, FAST, 91405 Orsay, France; (3) Gabriel Amselem, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France. Table of Links Abstract and Introduction Abstract and Introduction Methods Methods Results Results Model Model Discussion, Acknowledgements and References Discussion, Acknowledgements and References Supplementary Material Supplementary Material V. DISCUSSION We have shown experimentally that the change in phototactic behavior of C. reinhardtii can be due to its recent history of illumination. When exposed to two closely spaced, identical stimuli, the algae act as if they were time-integrating the stimuli. This is visible when the stimulus is close to that delimiting positive and negative phototaxis. Then, the algae show two different behaviors in response to the two consecutive stimuli: first a backand-forth response, then a negative phototaxis. When the stimuli are sufficiently spaced apart, the algae have had time to relax to a basal state, and show the same qualitative response to the two stimuli, see Fig. 6. In our experiments, we find this time of complete relaxation to be approximately equal to 30 minutes. A simplified model of phototaxis explains this memory effect by the introduction of a time-scale of relaxation in the inner biochemistry of the cell. When the time-scale of relaxation is larger than the time between two consecutive stimuli, the alga integrates the signal and can display different behaviors in response to the two identical stimuli, see Fig. 8. The time needed to return to the basal state should be of order 3τ , which underlies our choice of τ = 10 min for the relaxation time constant. Our experimental data are consistent with an inner relaxation time τ in the range ≈ 5 to 20 minutes. What could be the biochemical species corresponding to the intracellular species S introduced in the model? It is very likely that our simplified model compounds the dynamics of multiple biochemical species, activated sequentially in a signalling cascade. Still, it is known that the photoreceptors for phototaxis in C. reinhardtii are channelrhodopsins, that become phosphorylated within milliseconds after the application of a light stimulus. A high level of phosphorylated channelrhodopsin-1 (ChR1) in the cell correlates with a change from positive to negative phototaxis [11], much like a high level of activated S corresponds to negative phototaxis in our model. Moreover, the time scale of dephosphorylation of ChR1 in C. reinhardtii has been shown to be of the order of ≈ 5 to 15 minutes [11], which is compatible with our value of τ = 10 min. A possibility is therefore to identify S with ChR1. A more physical model of phototaxis was recently introduced by Leptos et al. to describe the response of C. reinhardtii to light [22]. In their model, Leptos et al. take into account the rotation of the microalga around its axis while swimming, and the resulting oscillating light intensity seen by the eyespot. The consecutive step-up and step-down stimuli sensed by the eyespot during one body rotation lead to a realignment of the trajectory towards the light source. Our model averages out the body rotation of the microalgae and describes the behavior of the microorganism at a more coarse-grained time-scale. Another difference is that the model of Leptos et al. does not take into account the fact that phototaxis changes sign when the light intensity increases. This change of phototactic behavior requires the introduction of a threshold value in the model, below (resp. above) which phototaxis is positive (resp. negative). Such a threshold is incorporated in our simplified model. Note that the threshold in the model, introduced as a simple means to obtain a change in behavior between positive and negative phototaxis at different light intensities, leads to the back-and-forth behavior at intermediate light intensities. The existence of this threshold also enables to explain why the time scale of negative phototaxis is longer than that of positive phototaxis. Negative phototaxis occurs when the amount of active species s ⋆ overcomes a threshold sT ; this takes time, during which the alga exhibits positive phototaxis. Only when s ⋆ > sT do the algae show negative phototaxis, and accumulate at one boundary of the well. The small initial positive phototactic response predicted by the model is in agreement with experimental data. The model also predicts that it is possible to switch the phototactic behavior of algae from positive phototaxis to back-and-forth to negative phototaxis, using three consecutive identical stimuli, by adjusting the waiting times between the stimuli and choosing carefully the stimulus intensity, see Fig. 8d. While we were not able to find the experimental conditions corresponding to this theoretical prediction, we were able to experimentally observe the switch from back-and-forth to negative phototaxis, and from positive phototaxis to back-and-forth in a couple experiments, see Supp. Fig. 5. While the model successfully reproduces the phototactic behavior and the time scales at play, it fails to reproduce two experimental observations. First, in a couple experiments, multiple consecutive back-and-forth of the center of mass were observed at intermediate intensities, see Supp. Fig. 6. Second, in experiments with consecutive stimuli at intermediate light intensities, algae in the third experiment (after a waiting time of 30 minutes) display positive phototaxis instead of the expected backand-forth behavior observed during the first experiment, see Fig. 6b and Supp. Fig. 5. Both behaviors can be obtained in the model by supposing that the threshold sT increases with the time spent under a light stimulus, and so depends on the history of the microorganism. Such an increasing threshold would also enable to recover the traditional adaptative behavior at longer time scales [15]. This implies having a third equation describing the timeevolution of sT , thus introducing another time constant into the problem. In the lab, the memory effects reported here imply that it is not possible to repeat the same phototaxis experiments on a given batch of cells and expect similar outcomes. Such an effect was already known in the case of long-term adaptation [15]. The data reported here show that even in the case of short-term experiments, the behavior is not necessarily reproducible. To study phototaxis quantitatively, experimental repeats should be carried out with different batches of naive cells. Having identified this short time-scale, our experiments pave the way for the study of phototaxis in the presence of timevarying light stimuli, much as the algae are subject to in their natural environment. There, light is constantly fluctuating. The short-term memory could then be a beneficial way to integrate a light signal randomly interrupted by the shadow of other motile organisms or objects. ACKNOWLEDGMENTS We thank David Gonzalez-Rodriguez for insightful comments on an early version of the model, Maxime Simon for preliminary experiments, Salome Guttierez Ramos for help with microfabrication, and Caroline Frot for precious technical support. This work was supported by “Investissements d’Avenir” LabEx PALM (ANR-10- LABX-0039-PALM) and by PEPS “M´ecanique du futur”. References [1] G. J´ekely, Philosophical Transactions of the Royal Society B: Biological Sciences 364, 2795 (2009). [2] K. W. Foster and R. D. Smyth, Microbiological reviews 44, 572 (1980). [3] P. Hegemann and P. 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