We refine Cohen and Lustig's description of centralisers of Dehn twists of free groups. We show that the centraliser of a Dehn twist of a free group has a subgroup of finite index that has a finite classifying space. We describe an algorithm to find a presentation of the centraliser. We use this algorithm to give an ex…
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FACMAC combines deep policy gradients with factored critic for multi-agent reinforcement learning.
problem Cooperative multi-agent reinforcement learning in discrete and continuous action spaces.
method FACMAC uses a centralised but factored critic, combining per-agent utilities into a joint action-value function.
result FACMAC outperforms MADDPG and other baselines on multi-agent particle environments and StarCraft II tasks.
The virtually cyclic dimension of Out(F_N) is finite and related properties are established.
problem Understanding the virtually cyclic dimension of Out(F_N) and related properties.
method Proving properties of finite index congruence subgroups and using exact sequences.
result The virtually cyclic dimension of Out(F_N) is finite.
The paper studies algebraic structures related to quantum groups.
problem Understanding centralisers of tensor representations of .
method Introducing fused permutations and braids, proving Schur--Weyl duality, and describing centralisers.
result A conjecture about a generating element of centralisers is proven in some cases.
Study of automorphisms and splittings of special groups, showing infinite groups under certain conditions.
problem Understanding the structure and automorphisms of special groups .
method Constructing and analyzing non-small, stable -actions on -trees.
result Conditions for the existence of infinite-order automorphisms and splittings.
Centralisers and Hecke algebras in Representation Theory, with applications to Knots and Physicsmath.RT
The thesis explores centralisers and Hecke algebras in representation theory with applications to knots and physics.
problem Understanding centralisers and Hecke algebras in representation theory.
method Review of classical and quantum Schur-Weyl duality, discussion of quantum groups and their centralisers, and application to knot theory and physics.
result New insights into centralisers and Hecke algebras, leading to solutions for the Yang-Baxter equation and link invariants.
This paper introduces a new metric to improve the performance of AMMs over centralised exchanges.
problem Lack of a precise metric to compare AMM performance with centralised exchanges.
method Introduces Rebalancing-versus-Rebalancing (RVR) to measure AMM performance more accurately.
result AMMs can offer superior execution and rebalancing efficiency compared to centralised exchanges, even with low fees.
In many real-world settings, a team of agents must coordinate their behaviour while acting in a decentralised way. At the same time, it is often possible to train the agents in a centralised fashion in a simulated or laboratory setting, where global state information is available and communication constraints are lifte…
QMIX combines per-agent values to create decentralised policies.
problem Training decentralised policies from centralised learning.
method QMIX uses a mixing network to estimate joint action-values as a monotonic combination of per-agent values.
result QMIX significantly outperforms existing methods on the StarCraft Multi-Agent Challenge (SMAC).
We introduce the palindromic automorphism group and the palindromic Torelli group of a right-angled Artin group A_G. The palindromic automorphism group Pi A_G is related to the principal congruence subgroups of GL(n,Z) and to the hyperelliptic mapping class group of an oriented surface, and sits inside the centraliser …
The paper presents methods to write presentations for Dehn quandles.
problem Writing explicit presentations for Dehn quandles.
method Two approaches: for Garside and Gaussian groups, and for general Dehn quandles with known centralisers.
result Examples of Dehn quandles including spherical Artin groups, surface groups, and mapping class groups.
A combinatorial description of the centralizer algebras connected to the Links-Gould Invariantmath.QA
In this paper we study the tensor powers of the standard representation of the quantum super-algebra , focusing on the rings of its algebra endomorphisms, called centraliser algebras and denoted by . Their dimensions were conjectured by I. Marin and E. Wagner \cite{MW}. We prove this conjecture, desc…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity, and smoothness, we establish statistical learning rates that retain, up to logari…
Study growth rates of automorphisms of special groups.
problem Understanding the growth rates of automorphisms of special groups.
method Analyzing outer automorphisms of virtually special groups, showing polynomial or exponential growth, and constructing Nielsen-Thurston decompositions.
result Outer automorphism groups of virtually special groups are boundary amenable, have finite virtual cohomological dimension, and satisfy the Tits alternative.
FTX's failure linked to Terra-Luna collapse and Binance's influence.
problem FTX's collapse due to misuse of native token and reliance on leverage.
method Analyzed on-chain data, studied cryptocurrency dependency structures, and examined public trades.
result FTX's downfall was accelerated by Binance's tweets and public reaction.
We describe a new class of holonomy groups on pseudo-Riemannian manifolds. Namely, we prove the following theorem. Let g be a nondegenerate bilinear form on a vector space V, and L:V -> V a g-symmetric operator. Then the identity component of the centraliser of L in SO(g) is a holonomy group for a suitable Levi-Civita …
Deep RL agent secures 2nd place in CityLearn Challenge for district demand management.
problem Optimizing electrical demand of diverse buildings in a district.
method Centralised 'Soft Actor Critic' deep reinforcement learning agent.
result Achieved an averaged score of 0.967 on challenge dataset.
This work uses reinforcement learning to optimize task scheduling and execution in a dynamic multi-agent warehouse environment.
problem Optimizing task scheduling and execution in a dynamic multi-agent warehouse environment with limited observability.
method Deep reinforcement learning to solve both high-level scheduling and low-level multi-agent execution problems.
result Demonstrates the effectiveness of reinforcement learning in optimizing task scheduling and execution in a dynamic multi-agent environment.
Finite order elements with infinite centralizers in 3-manifold groups imply specific structure.
problem Understanding centralizers of torsion elements in 3-manifold groups.
method Analyzing -complexes and applying the Projective Plane Theorem.
result 3-manifolds with specific properties (e.g., ) arise from certain centralizer conditions.
Static Replication of Impermanent Loss for Concentrated Liquidity Provision in Decentralised Marketsq-fin.GN
The article provides formulas to hedge impermanent loss in decentralized markets.
problem Impermanent loss in concentrated liquidity provision in decentralized markets.
method Analytical characterizations and static replication formulas using European calls or puts.
result Static replication formulas accurately hedge impermanent loss.
The paper studies the action of automorphisms on train tracks and finds that the set of minimally displaced points is co-compact.
problem The study of automorphisms and their action on train tracks in free products.
method Analysis of train track points and minimally displaced set under cyclic subgroup generated by automorphisms.
result The minimally displaced set is co-compact under the action of the cyclic subgroup generated by the automorphism.
Blockchain offers a decentralized, immutable, transparent system of records. It offers a peer-to-peer network of nodes with no centralised governing entity making it unhackable and therefore, more secure than the traditional paper-based or centralised system of records like banks etc. While there are certain advantages…
Fix a simple complex Lie group G and a principal sl(2,C) subalgebra of Lie(G). Then the moduli space of semi-stable, topologically trivial G-Higgs bundles on a hyperbolic, spin Riemann surface acquires a marked point. This is the unique C*-fixed point on the Hitchin section. We describe a universal analytic family of d…
Machine learning models can be used for pattern recognition in medical data in order to improve patient outcomes, such as the prediction of in-hospital mortality. Deep learning models, in particular, require large amounts of data for model training. However, the data is often collected at different hospitals and sharin…
We provide two distributed confidence ball algorithms for solving linear bandit problems in peer to peer networks with limited communication capabilities. For the first, we assume that all the peers are solving the same linear bandit problem, and prove that our algorithm achieves the optimal asymptotic regret rate of a…
Let t_a be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, I(t_a^n(b),b)=|n|I(a,b)^2, where I(,) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties o…
Garside groupoids, as recently introduced by Krammer, generalise Garside groups. A weak Garside group is a group that is equivalent as a category to a Garside groupoid. We show that any periodic loop in a Garside groupoid $\CG$ may be viewed as a Garside element for a certain Garside structure on another Garside groupo…
Optimizes trading in CFMMs and exchanges using deep learning.
problem Optimizing trading strategies in CFMMs and exchanges.
method Develops a model accounting for interaction between CFMMs and exchanges, employs deep Galerkin method to solve dynamic programming equation.
result Optimal strategy outperforms naïve strategies and is not prone to price slippage.
Study on conformal transformations of Cahen-Wallach spaces, focusing on fixed points and discontinuous groups.
problem Characterizing conformal transformations of Cahen-Wallach spaces.
method Analyzing conformal transformations of indecomposable Lorentzian symmetric spaces, focusing on fixed points and discontinuous groups.
result Essential conformal transformations of conformally curved Cahen-Wallach spaces have fixed points, and such transformations cannot centralize essential homotheties.
In many real-world applications of machine learning, data are distributed across many clients and cannot leave the devices they are stored on. Furthermore, each client's data, computational resources and communication constraints may be very different. This setting is known as federated learning, in which privacy is a …
Paper proves equivariant Fried conjecture for specific flows.
problem Equivariant Fried conjecture for suspension flows.
method Analyzes suspension flows of equivariant isometries.
result Proves conjecture for various groups and cases.
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not scale well to large graphs. We therefore propose a framework for parallel computat…
This work benchmarks MARL algorithms in cooperative tasks.
problem Lack of evaluation tasks and criteria for comparing MARL algorithms.
method Systematic evaluation of three MARL algorithm classes in diverse cooperative tasks.
result Insights into the effectiveness of different learning approaches.
We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of non positive curvature and which do not hold for arbitrary characteristic zero l…
DistGP models multi-robot mapping with distributed Gaussian process learning.
problem Collaborative mapping by multiple robots with limited local data.
method Sparse Gaussian process with factorisation and distributed training via GBP.
result DistGP achieves superior accuracy and robustness compared to DiNNO.
Generators found for automorphisms of special groups.
problem Characterizing automorphisms of special groups.
method Using a novel hierarchical shortening argument, the paper provides generators for automorphisms of special groups.
result Generators for automorphisms of special groups are found, including Dehn twists and pseudo-twists.
Centralised training with decentralised execution is an important setting for cooperative deep multi-agent reinforcement learning due to communication constraints during execution and computational tractability in training. In this paper, we analyse value-based methods that are known to have superior performance in com…
Word embeddings learnt from large corpora have been adopted in various applications in natural language processing and served as the general input representations to learning systems. Recently, a series of post-processing methods have been proposed to boost the performance of word embeddings on similarity comparison an…
Quantitative finance has had a long tradition of a bottom-up approach to complex systems inference via multi-agent systems (MAS). These statistical tools are based on modelling agents trading via a centralised order book, in order to emulate complex and diverse market phenomena. These past financial models have all rel…
A modular GP framework for efficient transfer learning.
problem Efficiently transfer knowledge across different tasks or datasets.
method Modular variational Gaussian processes (GPs) with a dictionary of well-fitted GPs.
result Reduces computational costs and allows the transfer of uncertainty metrics.
This study optimizes trading and arbitrage in decentralized finance's CPMs, revealing convexity costs and developing efficient strategies.
problem Optimizing trading and arbitrage in decentralized finance's constant product markets (CPMs).
method Developed models for CPMs in competing centralised exchanges, CPMs, and both venues. Derived computationally efficient strategies.
result Accurately estimated convexity costs in CPMs, which are linear in trade size and nonlinear in liquidity depth and exchange rate.
The blockchain technology promises to transform finance, money and even governments. However, analyses of blockchain applicability and robustness typically focus on isolated systems whose actors contribute mainly by running the consensus algorithm. Here, we highlight the importance of considering trustless platforms wi…
Improved fraud detection in finance with quantum-enhanced federated learning.
problem Challenges in detecting financial fraud with traditional methods.
method Hybrid quantum-enhanced federated learning framework combining quantum LSTM with privacy-preserving techniques.
result Approximately 5% improvement in performance metrics compared to conventional models.
Recent advances in the fields of machine learning and neurofinance have yielded new exciting research perspectives in practical inference of behavioural economy in financial markets and microstructure study. We here present the latest results from a recently published stock market simulator built around a multi-agent s…
OpenAlpha validates decentralized capital strategies using game theory and market aggregation.
problem Decentralized capital management's lack of trust-minimised, adaptive deployment.
method Game-theoretic validation, adversarial auditing, market-based belief aggregation.
result Confidence scores from validation phases inform capital allocation rules.
We study the problem of determining the isomorphism classes of the virtually cyclic subgroups of the n-string braid groups B_n(S^2) of the 2-sphere S^2. If n is odd, or if n is even and sufficiently large, we obtain the complete classification. For small even values of n, the classification is complete up to an explici…
We explore inverse and quanto inverse crypto options, their pricing, and applications.
problem Market incompleteness in crypto options trading.
method Comparison of direct and inverse options, and introduction of currency-protected 'quanto' options.
result Pricing and hedging characteristics of inverse and quanto inverse options in a Black-Scholes framework.
Cryptofinance generates yield through innovative decentralized finance.
problem Lack of intrinsic yield in crypto-assets.
method Analysis of yield-generating mechanisms in cryptofinance.
result Cryptofinance innovations enable yield generation through various decentralized and centralised mechanisms.