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

Anvendt økonomi for ledere – Globale perspektiver

Finanskrisen i 2008 sendte sjokkbølger gjennom alle verdensdeler, myndigheter, finans- og bankbransjer og hos folk flest. Uro, panikk og en stor grad av håpløshet spredte seg til alle verdenshjørner, og mange fryktet det verste. Det er denne perioden, fra rundt 2008 til 2009, vi skal ta for oss i denne oppgaven. En periode hvor Norge og verden opplevde negativ økonomisk vekst. På de neste fem sidene skal vi diskutere mulige årsaker til denne negative økonomiske veksten (SSB, 2021). Vil vi ta utgangspunkt i realligningen og anvende AD-AS modellen som et rammeverk for vår makroøkonomiske analyse. I første del vil vi redegjøre for realligningen og de faktorene som spiller inn i en nasjonal økonomi, samt AD-AS modellen og forklare hvordan tilbud- og etterspørselssiden henger sammen og beskrive generelle prinsipper ved kurvens skifter. I neste del vil vi anvende teorien til å diskutere årsaker til negativ økonomisk vekst i Norge i perioden 2008-2009, hvor vi særlig vil vektlegge hvorvidt den negative økonomiske veksten hadde med forhold på tilbudssiden og/eller etterspørselssiden å gjøre. Deretter vil vi diskutere funnene våre i forhold til hva økonomer antar er typiske trekk når det gjelder etterspørselsfaktorens utvikling i krisetider. Vi vil så se på hva myndighetene kunne gjøre for å kontre den negative økonomiske veksten, før vi kommenterer om funnene våre antyder om beslutningstakerne eller politikerne er inspirert av noen kjente økonomer. Helt til slutt vil vi oppsummere funnene våre og avslutter med en konklusjon

On the distribution of the number of customers in the symmetric M/G/1 queue

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella, Zwart and Boxma [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty. In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a counterexample, involving the hyperexponential distribution, that the conjecture is generally not true

Producing Synthetic Dataset for Human Fall Detection in AR/VR Environments

Human poses and the behaviour estimation for different activities in (virtual reality/augmented reality) VR/AR could have numerous beneficial applications. Human fall monitoring is especially important for elderly people and for non-typical activities with VR/AR applications. There are a lot of different approaches to improving the fidelity of fall monitoring systems through the use of novel sensors and deep learning architectures; however, there is still a lack of detail and diverse datasets for training deep learning fall detectors using monocular images. The issues with synthetic data generation based on digital human simulation were implemented and examined using the Unreal Engine. The proposed pipeline provides automatic “playback” of various scenarios for digital human behaviour simulation, and the result of a proposed modular pipeline for synthetic data generation of digital human interaction with the 3D environments is demonstrated in this paper. We used the generated synthetic data to train the Mask R-CNN-based segmentation of the falling person interaction area. It is shown that, by training the model with simulation data, it is possible to recognize a falling person with an accuracy of 97.6% and classify the type of person’s interaction impact. The proposed approach also allows for covering a variety of scenarios that can have a positive effect at a deep learning training stage in other human action estimation tasks in an VR/AR environment

Novel Bis-Ammonium Salts of Pyridoxine: Synthesis and Antimicrobial Properties

A series of 108 novel quaternary bis-ammonium pyridoxine derivatives carrying various substituents at the quaternary nitrogen’s and acetal carbon was synthesized. Thirteen compounds exhibited antibacterial and antifungal activity (minimum inhibitory concentration (MIC) 0.25–16 µg/mL) comparable or superior than miramistin, benzalkonium chloride, and chlorhexidine. A strong correlation between the lipophilicity and antibacterial activity was found. The most active compounds had logP values in the range of 1–3, while compounds with logP > 6 and logP < 0 were almost inactive. All active compounds demonstrated cytotoxicity comparable with miramistin and chlorhexidine on HEK-293 cells and were three-fold less toxic when compared to benzalkonium chloride. The antibacterial activity of leading compound 5c12 on biofilm-embedded Staphylococcus aureus, Staphylococcus epidermidis, Escherichia coli or Pseudomonas aeruginosa was comparable or even higher than that of the benzalkonium chloride. In vivo 5c12 was considerably less toxic (LD50 1705 mg/kg) than benzalkonium chloride, miramistine, and chlorhexidine at oral administration on CD-1 mice. An aqueous solution of 5c12 (0.2%) was shown to be comparable to reference drugs efficiency on the rat’s skin model. The molecular target of 5c12 seems to be a cellular membrane as other quaternary ammonium salts. The obtained results make the described quaternary bis-ammonium pyridoxine derivatives promising and lead molecules in the development of the new antiseptics with a broad spectrum of antimicrobial activity