19,933 research outputs found
A hierarchy of local decision
We extend the notion of distributed decision in the framework of distributed network computing, inspired by both the polynomial hierarchy for Turing machines and recent results on so-called distributed graph automata. We show that, by using distributed decision mechanisms based on the interaction between a prover and a disprover, the size of the certificates distributed to the nodes for certifying a given network property can be drastically reduced. For instance, we prove that minimum spanning tree (MST) can be certified with O(logâĄn)-bit certificates in n-node graphs, with just one interaction between the prover and the disprover, while it is known that certifying MST requires Ω(log2âĄn)-bit certificates if only the prover can act. The improvement can even be exponential for some simple graph properties. For instance, it is known that certifying the existence of a nontrivial automorphism requires Ω(n2) bits if only the prover can act. We show that there is a protocol with two interactions between the prover and the disprover that certifies nontrivial automorphism with O(logâĄn)-bit certificates. These results are achieved by defining and analyzing a local hierarchy of decision which generalizes the classical notions of proof-labeling schemes and locally checkable proofs.Peer reviewe
Meso-scale FDM material layout design strategies under manufacturability constraints and fracture conditions
In the manufacturability-driven design (MDD) perspective, manufacturability of the product or system is the most important of the design requirements. In addition to being able to ensure that complex designs (e.g., topology optimization) are manufacturable with a given process or process family, MDD also helps mechanical designers to take advantage of unique process-material effects generated during manufacturing. One of the most recognizable examples of this comes from the scanning-type family of additive manufacturing (AM) processes; the most notable and familiar member of this family is the fused deposition modeling (FDM) or fused filament fabrication (FFF) process. This process works by selectively depositing uniform, approximately isotropic beads or elements of molten thermoplastic material (typically structural engineering plastics) in a series of pre-specified traces to build each layer of the part. There are many interesting 2-D and 3-D mechanical design problems that can be explored by designing the layout of these elements. The resulting structured, hierarchical material (which is both manufacturable and customized layer-by-layer within the limits of the process and material) can be defined as a manufacturing process-driven structured material (MPDSM). This dissertation explores several practical methods for designing these element layouts for 2-D and 3-D meso-scale mechanical problems, focusing ultimately on design-for-fracture. Three different fracture conditions are explored: (1) cases where a crack must be prevented or stopped, (2) cases where the crack must be encouraged or accelerated, and (3) cases where cracks must grow in a simple pre-determined pattern. Several new design tools, including a mapping method for the FDM manufacturability constraints, three major literature reviews, the collection, organization, and analysis of several large (qualitative and quantitative) multi-scale datasets on the fracture behavior of FDM-processed materials, some new experimental equipment, and the refinement of a fast and simple g-code generator based on commercially-available software, were developed and refined to support the design of MPDSMs under fracture conditions. The refined design method and rules were experimentally validated using a series of case studies (involving both design and physical testing of the designs) at the end of the dissertation. Finally, a simple design guide for practicing engineers who are not experts in advanced solid mechanics nor process-tailored materials was developed from the results of this project.U of I OnlyAuthor's request
Emergence simulation of cell-like morphologies with evolutionary potential by virtual molecular interactions
This study explores the emergence of life through a simulation model
approach. The model "Multi-set chemical lattice model" is a model that allows
virtual molecules of multiple types to be placed in each lattice cell on a
two-dimensional space. This model is capable of describing a wide variety of
states and interactions in a limited number of lattice cell spaces, such as
diffusion, chemical reaction, and polymerization of virtual molecules. This
model is also capable of describing a wide variety of states and interactions
even in the limited lattice cell space of 100 x 100 cells. Furthermore it was
considered energy metabolism and energy resources environment. It was able to
reproduce the "evolution" in which a certain cell-like shapes adapted to the
environment survives under conditions of decreasing amounts of energy resources
in the environment. This enabled the emergence of cell-like shapes with the
four minimum cellular requirements: boundary, metabolism, replication, and
evolution, based solely on the interaction of virtual molecules.Comment: arXiv admin note: text overlap with arXiv:2204.0968
Barren plateaus in quantum tensor network optimization
We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer
Communicating Actor Automata -- Modelling Erlang Processes as Communicating Machines
Brand and Zafiropulo's notion of Communicating Finite-State Machines (CFSMs)
provides a succinct and powerful model of message-passing concurrency, based
around channels. However, a major variant of message-passing concurrency is not
readily captured by CFSMs: the actor model. In this work, we define a variant
of CFSMs, called Communicating Actor Automata, to capture the actor model of
concurrency as provided by Erlang: with mailboxes, from which messages are
received according to repeated application of pattern matching. Furthermore,
this variant of CFSMs supports dynamic process topologies, capturing common
programming idioms in the context of actor-based message-passing concurrency.
This gives a new basis for modelling, specifying, and verifying Erlang
programs. We also consider a class of CAAs that give rise to freedom from race
conditions.Comment: In Proceedings PLACES 2023, arXiv:2304.0543
High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descent
In this paper, we study differentially private empirical risk minimization
(DP-ERM). It has been shown that the worst-case utility of DP-ERM reduces
polynomially as the dimension increases. This is a major obstacle to privately
learning large machine learning models. In high dimension, it is common for
some model's parameters to carry more information than others. To exploit this,
we propose a differentially private greedy coordinate descent (DP-GCD)
algorithm. At each iteration, DP-GCD privately performs a coordinate-wise
gradient step along the gradients' (approximately) greatest entry. We show
theoretically that DP-GCD can achieve a logarithmic dependence on the dimension
for a wide range of problems by naturally exploiting their structural
properties (such as quasi-sparse solutions). We illustrate this behavior
numerically, both on synthetic and real datasets
Satisfiability of Non-Linear Transcendental Arithmetic as a Certificate Search Problem
For typical first-order logical theories, satisfying assignments have a
straightforward finite representation that can directly serve as a certificate
that a given assignment satisfies the given formula. For non-linear real
arithmetic with transcendental functions, however, no general finite
representation of satisfying assignments is available. Hence, in this paper, we
introduce a different form of satisfiability certificate for this theory,
formulate the satisfiability verification problem as the problem of searching
for such a certificate, and show how to perform this search in a systematic
fashion. This does not only ease the independent verification of results, but
also allows the systematic design of new, efficient search techniques.
Computational experiments document that the resulting method is able to prove
satisfiability of a substantially higher number of benchmark problems than
existing methods
Temporal and spatial change of habitat quality and its driving forces: The case of Tacheng region, China
Habitat quality assessment is an important basis for ecological restoration practice. Taking the Tacheng region as an example, the InVEST model was used to evaluate the habitat quality of the Tacheng region in five periods from 2000 to 2020, and analyze the reasons for its changes, to provide theoretical guidance for ecological restoration practice in arid areas. The conclusions were that from 2000 to 2020, the habitat quality in the Tacheng region improved slightly, and the value of the habitat index in the Tacheng region was the highest in 2010, which was 0.577, and then decreased slightly. The habitat quality in the Tacheng region was significantly influenced by land use type conversion and precipitation. The change in land use type directly affected the change in habitat quality. The study region is located in an arid area; the forest land and grassland native to the region have more vegetation communities and genera of species and can be self-sustaining and resilient to disturbance, having high scores for habitat quality. The species of arable land is a monoculture; it cannot be self-sustaining and resilient to disturbance, and though it has high vegetation cover, the value of habitat quality is lower than that of forestland and grassland. The vegetation of unused land is rare, and the ecosystem of unused land is sensitive and vulnerable; the habitat quality scores are very low. The conversion of forest land, grassland, arable land, and unused land would directly affect the value of habitat quality, and conversion was the main factor affecting the change in habitat quality. In addition, precipitation was also an important factor affecting the change in habitat quality in the Tacheng region, which affected the biomass of natural vegetation and then affected the habitat quality. The results provided the temporal and spatial change of habitat quality and its driving forces in the Tacheng region, which helps determine appropriate measures and sites in ecological restoration projects
Floquet codes and phases in twist-defect networks
We introduce a class of models, dubbed paired twist-defect networks, that
generalize the structure of Kitaev's honeycomb model for which there is a
direct equivalence between: i) Floquet codes (FCs), ii) adiabatic loops of
gapped Hamiltonians, and iii) unitary loops or Floquet-enriched topological
orders (FETs) many-body localized phases. This formalism allows one to apply
well-characterized topological index theorems for FETs to understand the
dynamics of FCs, and to rapidly assess the code properties of many FC models.
As an application, we show that the Honeycomb Floquet code of Haah and Hastings
is governed by an irrational value of the chiral Floquet index, which implies a
topological obstruction to forming a simple, logical boundary with the same
periodicity as the bulk measurement schedule. In addition, we construct
generalizations of the Honeycomb Floquet code exhibiting arbitrary
anyon-automorphism dynamics for general types of Abelian topological order.Comment: 17+5 pages, 10 figure
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