arXiv research

Two proofs show that removing a loop from a plane circuit splits the plane.

Call {\em i-hedrite} any 4-valent n-vertex plane graph, whose faces are 2-, 3- and 4-gons only and $p_2+p_3=i$. The edges of an i-hedrite, as of any Eulerian plane graph, are partitioned by its {\em central circuits}, i.e. those, which are obtained by starting with an edge and continuing at each vertex by the edge oppo…

We consider here 6-regular plane graphs whose faces have size 1, 2 or 3. In Section 2 a practical enumeration method is given that allowed us to enumerate them up to 53 vertices. Subsequently, in Section 3 we enumerate all possible symmetry groups of the spheres that showed up. In Section 4 we introduce a new Goldberg-…

The lattice stick number $s_L(L)$ of a link $L$ is defined to be the minimal number of straight line segments required to construct a stick presentation of $L$ in the cubic lattice. Hong, No and Oh found a general upper bound $s_L(K) \leq 3 c(K) +2$. A rational link can be represented by a lattice presentation with exa…

A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face. A railroad in a plane graph is a circuit of hexagonal faces, such that any hexagon is adjacent to its neighbors on opposite edges. A graph without a railroad is called tight. We consider the zigz…

A central problem in neuroscience is reconstructing neuronal circuits on the synapse level. Due to a wide range of scales in brain architecture such reconstruction requires imaging that is both high-resolution and high-throughput. Existing electron microscopy (EM) techniques possess required resolution in the lateral p…

Study evaluates capacity and trainability of parametrized quantum circuits.

Let $D$ be an oriented classical or virtual link diagram with directed universe $\vec{U}$. Let $C$ denote a set of directed Euler circuits, one in each connected component of $U$. There is then an associated looped interlacement graph $L(D,C)$ whose construction involves very little geometric information about the way …

The paper tests if LLMs' capabilities are executed by small subnetworks (circuits).

Study detects if a circuit bounds a disc using curve intersections.

Evolutionary strategy optimizes quantum circuit design and parameters.

An i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all i-hedrites and the minimal representative for each. We also review the link of 4-hed…

This work uses SVM to identify track component failures in AC Track Circuits.

The statistical complexity of quantum circuits is studied using Rademacher complexity.

Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum circuits exhibit stronger expressibility compared to classical neural networks. O…

Quantum mechanics is inherently probabilistic in light of Born's rule. Using quantum circuits as probabilistic generative models for classical data exploits their superior expressibility and efficient direct sampling ability. However, training of quantum circuits can be more challenging compared to classical neural net…

The study examines how quantum resources enhance the complexity of quantum circuits.

A new approach uses circuit topology to study complex polymer interactions.

Study bounds VAR model's circuit complexity, showing it's limited to TC^0 circuits.

In this work, a machine learning approach for identifying the multi-omics metabolic regulatory control circuits inside the pathways is described. Therefore, the identification of bacterial metabolic pathways that are more regulated than others in term of their multi-omics follows from the analysis of these circuits . T…

Study shows limitations and possibilities of learning quantum circuit output distributions.

Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by …

We constructed an analog electrical circuit which generates fluctuations in which probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by adjusting the resistance. With this low cost circuit the random fluctuations which have the simil…

Spin networks boost quantum algorithms solving SU(2) symmetric problems.

Enhances quantum circuit synthesis using deep learning and geometric methods.

Single T-gate makes distribution learning hard for deep circuits.

We propose a neural information processing system which is obtained by re-purposing the function of a biological neural circuit model, to govern simulated and real-world control tasks. Inspired by the structure of the nervous system of the soil-worm, C. elegans, we introduce Neuronal Circuit Policies (NCPs), defined as…

Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves …

Quantum circuits are hard to learn on average.

Study improves probabilistic circuits using transformations for better predictions.

Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (eg, radiation effects) into an existing compact model is not triv…

Quantum circuit optimization speeds up financial derivatives pricing.

Bayesian approach optimizes quantum circuits for noisy hardware.

The state-of-the-art machine learning approaches are based on classical von Neumann computing architectures and have been widely used in many industrial and academic domains. With the recent development of quantum computing, researchers and tech-giants have attempted new quantum circuits for machine learning tasks. How…

Complex frequency generalizes eigenvalues in LTI systems.

Quantum variational circuits improve reinforcement learning efficiency.

Develops a braid-theoretic framework to analyze chirality in molecular knots.

PNCs balance tractability and expressiveness in probabilistic modeling.

Unified tractability conditions for various compositional inference queries.

Quantum circuits predict volatility dynamics preserving asymmetry.

Active sampling improves design space exploration for analog circuits.

Quantum circuits explained using Shapley values for better understanding.

Quantum neural tangent kernels help understand variational quantum circuits in machine learning.

Geometrically interprets frequency in electric circuits.

Unified framework for tractable inference scenarios in machine learning models.

Quantum circuit models learn better with specific initialization strategies.

A quantum model classifies financial sentiment by mapping text chunks to quantum circuits.

A quantum circuit designed for efficient statistical model preparation and training.