471 research outputs found
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning
The paper introduces the application of information geometry to describe the
ground states of Ising models by utilizing parity-check matrices of cyclic and
quasi-cyclic codes on toric and spherical topologies. The approach establishes
a connection between machine learning and error-correcting coding. This
proposed approach has implications for the development of new embedding methods
based on trapping sets. Statistical physics and number geometry applied for
optimize error-correcting codes, leading to these embedding and sparse
factorization methods. The paper establishes a direct connection between DNN
architecture and error-correcting coding by demonstrating how state-of-the-art
architectures (ChordMixer, Mega, Mega-chunk, CDIL, ...) from the long-range
arena can be equivalent to of block and convolutional LDPC codes (Cage-graph,
Repeat Accumulate). QC codes correspond to certain types of chemical elements,
with the carbon element being represented by the mixed automorphism
Shu-Lin-Fossorier QC-LDPC code. The connections between Belief Propagation and
the Permanent, Bethe-Permanent, Nishimori Temperature, and Bethe-Hessian Matrix
are elaborated upon in detail. The Quantum Approximate Optimization Algorithm
(QAOA) used in the Sherrington-Kirkpatrick Ising model can be seen as analogous
to the back-propagation loss function landscape in training DNNs. This
similarity creates a comparable problem with TS pseudo-codeword, resembling the
belief propagation method. Additionally, the layer depth in QAOA correlates to
the number of decoding belief propagation iterations in the Wiberg decoding
tree. Overall, this work has the potential to advance multiple fields, from
Information Theory, DNN architecture design (sparse and structured prior graph
topology), efficient hardware design for Quantum and Classical DPU/TPU (graph,
quantize and shift register architect.) to Materials Science and beyond.Comment: 71 pages, 42 Figures, 1 Table, 1 Appendix. arXiv admin note: text
overlap with arXiv:2109.08184 by other author
Noncommutative Geometry and Gauge theories on AF algebras
Non-commutative geometry (NCG) is a mathematical discipline developed in the
1990s by Alain Connes. It is presented as a new generalization of usual
geometry, both encompassing and going beyond the Riemannian framework, within a
purely algebraic formalism. Like Riemannian geometry, NCG also has links with
physics. Indeed, NCG provided a powerful framework for the reformulation of the
Standard Model of Particle Physics (SMPP), taking into account General
Relativity, in a single "geometric" representation, based on Non-Commutative
Gauge Theories (NCGFT). Moreover, this accomplishment provides a convenient
framework to study various possibilities to go beyond the SMPP, such as Grand
Unified Theories (GUTs). This thesis intends to show an elegant method recently
developed by Thierry Masson and myself, which proposes a general scheme to
elaborate GUTs in the framework of NCGFTs. This concerns the study of NCGFTs
based on approximately finite -algebras (AF-algebras), using either
derivations of the algebra or spectral triples to build up the underlying
differential structure of the Gauge Theory. The inductive sequence defining the
AF-algebra is used to allow the construction of a sequence of NCGFTs of
Yang-Mills Higgs types, so that the rank can represent a grand unified
theory of the rank . The main advantage of this framework is that it
controls, using appropriate conditions, the interaction of the degrees of
freedom along the inductive sequence on the AF algebra. This suggests a way to
obtain GUT-like models while offering many directions of theoretical
investigation to go beyond the SMPP
Operational Research: methods and applications
This is the final version. Available on open access from Taylor & Francis via the DOI in this recordThroughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes
Structured parallelism discovery with hybrid static-dynamic analysis and evaluation technique
Parallel computer architectures have dominated the computing landscape for the
past two decades; a trend that is only expected to continue and intensify, with increasing specialization and heterogeneity. This creates huge pressure across the software
stack to produce programming languages, libraries, frameworks and tools which will
efficiently exploit the capabilities of parallel computers, not only for new software, but
also revitalizing existing sequential code. Automatic parallelization, despite decades of
research, has had limited success in transforming sequential software to take advantage
of efficient parallel execution. This thesis investigates three approaches that use commutativity analysis as the enabler for parallelization. This has the potential to overcome
limitations of traditional techniques.
We introduce the concept of liveness-based commutativity for sequential loops.
We examine the use of a practical analysis utilizing liveness-based commutativity in a
symbolic execution framework. Symbolic execution represents input values as groups
of constraints, consequently deriving the output as a function of the input and enabling
the identification of further program properties. We employ this feature to develop an
analysis and discern commutativity properties between loop iterations. We study the
application of this approach on loops taken from real-world programs in the OLDEN
and NAS Parallel Benchmark (NPB) suites, and identify its limitations and related
overheads.
Informed by these findings, we develop Dynamic Commutativity Analysis (DCA), a
new technique that leverages profiling information from program execution with specific
input sets. Using profiling information, we track liveness information and detect loop
commutativity by examining the code’s live-out values. We evaluate DCA against almost
1400 loops of the NPB suite, discovering 86% of them as parallelizable. Comparing
our results against dependence-based methods, we match the detection efficacy of two
dynamic and outperform three static approaches, respectively. Additionally, DCA is
able to automatically detect parallelism in loops which iterate over Pointer-Linked
Data Structures (PLDSs), taken from wide range of benchmarks used in the literature,
where all other techniques we considered failed. Parallelizing the discovered loops, our
methodology achieves an average speedup of 3.6× across NPB (and up to 55×) and up
to 36.9× for the PLDS-based loops on a 72-core host. We also demonstrate that our
methodology, despite relying on specific input values for profiling each program, is able
to correctly identify parallelism that is valid for all potential input sets.
Lastly, we develop a methodology to utilize liveness-based commutativity, as implemented in DCA, to detect latent loop parallelism in the shape of patterns. Our approach
applies a series of transformations which subsequently enable multiple applications
of DCA over the generated multi-loop code section and match its loop commutativity
outcomes against the expected criteria for each pattern. Applying our methodology on
sets of sequential loops, we are able to identify well-known parallel patterns (i.e., maps,
reduction and scans). This extends the scope of parallelism detection to loops, such
as those performing scan operations, which cannot be determined as parallelizable by
simply evaluating liveness-based commutativity conditions on their original form
Operational research:methods and applications
Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order
Algebraic and Geometric Characterizations Related to the Quantization Problem of the Channel
In this paper, we consider the steps to be followed in the analysis and
interpretation of the quantization problem related to the channel,
where the Fuchsian differential equations, the generators of the Fuchsian
groups, and the tessellations associated with the cases and ,
related to the hyperbolic case, are determined. In order to obtain these
results, it is necessary to determine the genus of each surface on which
this channel may be embedded. After that, the procedure is to determine the
algebraic structure (Fuchsian group generators) associated with the fundamental
region of each surface. To achieve this goal, an associated linear second-order
Fuchsian differential equation whose linearly independent solutions provide the
generators of this Fuchsian group is devised. In addition, the tessellations
associated with each analyzed case are identified. These structures are
identified in four situations, divided into two cases and ,
obtaining, therefore, both algebraic and geometric characterizations associated
with quantizing the channel.Comment: 31 pages, 9 figure
Honeycomb Layered Frameworks with Metallophilic Bilayers
Honeycomb layered frameworks with metallophilic bilayers have garnered
traction in various disciplines due to their unique configuration and numerous
physicochemical and topological properties, such as fast ionic conduction,
coordination chemistry, and structural defects. These properties make them
attractive for energy storage applications, leading to increased attention
towards their metallophilic bilayer arrangements. This Review focuses on recent
advancements in this field, including characterisation techniques like X-ray
absorption spectroscopy and high-resolution transmission electron microscopy,
particularly for silver-based oxides. It also highlights strategies related to
cationic-deficient phases induced by topology or temperature, expanding the
compositional space of honeycomb layered frameworks with a focus on cationic
bilayer architectures. The Review further discusses theoretical approaches for
understanding the bilayered structure, especially concerning critical phenomena
at the monolayer-bilayer phase transition. Honeycomb layered frameworks are
described as optimised lattices within the congruent sphere packing problem,
equivalent to a specific two-dimensional conformal field theory. The
monolayer-bilayer phase transition involves a 2D-to-3D crossover. Overall, this
Review aims to provide a panoramic view of honeycomb layered frameworks with
metallophilic bilayers and their potential applications in the emerging field
of quantum matter. It is valuable for recent graduates and experts alike across
diverse fields, extending beyond materials science and chemistry.Comment: 68 pages, 24 figure
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