19 papers · ranked by Valyu relevance
S. Romano, A. Salles, M. Amalric, S. Dehaene + 2 more
Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of…
Kamaludin Dingle, Chico Q. Camargo, Ard A. Louis
Many systems in nature can be described using discrete input-output maps. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. Here, by extending fundamental results from algorithmic information…
Yuval Filmus
> Abstract. A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. We define a natural partial order on the set of codes, and show how to construct effectively a code better than a given sequence of…
Maximilian Gehri, Lukas Stelzl, Heinz Koeppl
Biochemical systems process signals through stochastic reaction dynamics that are inherently continuous in time and often exhibit memory, feedback, and nonequilibrium driving. At the same time, they are frequently modeled by effective reactions, e.g., multi-step processes such as transcription are treated as single…
Henk D. L. Hollmann, Patrick Solé
We construct a family of linear optimal functional-repair regenerating storage codes with parameters $({m,(n,k),(r,α,β)}={(2r-α+1)α/2,(r+1,r),(r,α,1)})$ for any integers $r,α$ with $1\leqα\leqr$, over any field when $α\in{1,r-1,r}$, and over any finite field $F_{q}$ with $q\geqr-1$ otherwise. These storage codes are…
Lihong Cao
The human brain encodes a virtually infinite repertoire of semantic concepts using a finite number of neurons, a feat that defies the capacity limits of classical attractor networks. While “Concept Cells” in the medial temporal lobe (MTL) exhibit extreme sparsity, the information-theoretic principles governing their…
Noga Alon, Boris Bukh, Yury Polyanskiy
We consider list-decoding in the zero-rate regime for two cases: the binary alphabet and the spherical codes in Euclidean space. Specifically, we study the maximal τ ∈ [0, 1] for which there exists an arrangement of M balls of relative Hamming radius τ in the binary hypercube (of arbitrary dimension) with the property…
Yeow Meng Chee, Tuvi Etzion, Han Mao Kiah, Alexander Vardy
High temperatures have dramatic negative effects on interconnect performance and, hence, numerous techniques have been proposed to reduce the power consumption of on-chip buses. However, existing methods fall short of fully addressing the thermal challenges posed by high-performance interconnects. In this paper, we…
Jesús Gutiérrez-Gutiérrez, Marta Zárraga-Rodríguez, Fernando M. Villar-Rosety, Xabier Insausti
'Fernando M. Villar-Rosety' 'Xabier Insausti'] In this paper, we give upper bounds for the rate-distortion function (RDF) of any Gaussian vector, and we propose coding strategies to achieve such bounds. We use these strategies to reduce the computational complexity of coding Gaussian asymptotically wide sense…
Anoop Thomas, Balaji Sundar Rajan
The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids. For vector linear index codes, discrete polymatroids, which can be viewed as a generalization of the matroids, were used. The index…
Beyza Dabak, Ahmed Hareedy, Robert Calderbank
The two-dimensional magnetic recording (TDMR) technology promises storage densities of 10 terabits per square inch. However, when tracks are squeezed together, a bit stored in the two-dimensional (TD) grid suffers inter-symbol interference (ISI) from adjacent bits in the same track, and inter-track interference (ITI)…
M. Ashok Kumar, Albert Sunny, Ashish Thakre, Ashisha Kumar + 3 more
'G. Dinesh Manohar' 'Nicusor Minculete' 'Shigeru Furuichi'] This paper establishes a close relationship among the four information theoretic problems, namely Campbell source coding, Arikan guessing, Huleihel et al. memoryless guessing and Bunte and Lapidoth tasks’ partitioning problems in the IID-lossless case. We…
R. Amzi Jeffs
We define a notion of morphism between combinatorial codes, making the class of all combinatorial codes into a category Code. We show that morphisms can be used to remove redundant information from a code, and that morphisms preserve convexity. This fact leads us to define "minimally non-convex" codes. We propose a…
Jesús Gutiérrez-Gutiérrez, Marta Zárraga-Rodríguez, Xabier Insausti
In this paper, we study the asymptotic optimality of a low-complexity coding strategy for Gaussian vector sources. Specifically, we study the convergence speed of the rate of such a coding strategy when it is used to encode the most relevant vector sources, namely wide sense stationary (WSS), moving average (MA), and…
Rodrick Wallace
The living state is cognitive at every scale and level of organization. Since it is possible to associate a broad class of cognitive processes with ‘dual’ information sources, many pathologies can be addressed using statistical models based on the Shannon Coding, the Shannon-McMillan Source Coding, the Rate Distortion…
Andrzej Chmielowiec, Paweł Litwin, Philip Broadbridge, Raúl Alcaraz
This article deals with compression of binary sequences with a given number of ones, which can also be considered as a list of indexes of a given length. The first part of the article shows that the entropy H of random n-element binary sequences with exactly k elements equal one satisfies the inequalities…
Miloje Rakočević
In some previous works (2018a,b; 2019, 2021a,b, 2022) we presented a new type of mirror symmetry, expressed in the set of protein amino acids; such a symmetry, that it simultaneously represents the semiotic essence of the genetic code. In this paper we provide new evidences that the genetic code represents the unity of…
Romain Brette
“Neural coding” is a popular metaphor in neuroscience, where objective properties of the world are communicated to the brain in the form of spikes. Here I argue that this metaphor is often inappropriate and misleading. First, when neurons are said to encode experimental parameters, the implied communication channel…
Zhenghong Chen
Persistent homology, building its foundation on homology theory, has been successfully applied various fields containing computation of topology. Here, we derive and implement persistent homology theory to specefic topological spaces with G-invariant covering, whereby persistence over quotient space can be canonically…