arXiv subjects

Simon Blackburn

Publications and source records attributed to Simon Blackburn.

7 recordsLinked to original sources

arXiv2025

On de Bruijn Array Codes Part II: Linear Codes

An M-sequence generated by a primitive polynomial has many interesting and desirable properties. A pseudo-random array is the two-dimensional generalization of an M-sequence. There are non-primitive polynomials all of whose non-zero sequences have the same period. These polynomials generate \emph{sets} of sequences with properties similar to M-sequences. In this paper, a two-dimensional generalization for such sequences is given. This generalization is for a pseudo-random array code, which is a set of $r_1 \times r_2$ arrays in which each $n_1 \times n_2$ nonzero matrix is contained exactly once as a window in one of the arrays. Moreover, these arrays have the shift-and-add property, i.e., the bitwise addition of two arrays (or a nontrivial shift of such arrays) is another array (or a shift of another array) from the code. All the known arrays can be formed by folding sequences generated from an irreducible polynomial or a reducible polynomial whose factors have the same degree and the same exponent. Two proof techniques are used to prove the constructions are indeed of pseudo-random array codes. The first technique is based on another method, different from folding, for constructing some of these arrays. The second technique is a generalization of a known proof technique. This generalization enables the construction of pseudo-random arrays with parameters not known before, and also provides a variety of pseudo-random array codes which cannot be generated by the first method. The two techniques also suggest two different hierarchies between pseudo-random array codes. Finally, two methods to verify whether a folding of sequences, generated by these polynomials, yields a pseudo-random array or a pseudo-random array code, will be presented.

cs.IT↗

arXiv2024

Large Scale Raman Spectrum Calculations in Defective 2D Materials using Deep Learning

We introduce a machine learning prediction workflow to study the impact of defects on the Raman response of 2D materials. By combining the use of machine-learned interatomic potentials, the Raman-active $\Gamma$-weighted density of states method and splitting configurations in independant patches, we are able to reach simulation sizes in the tens of thousands of atoms, with diagonalization now being the main bottleneck of the simulation. We apply the method to two systems, isotopic graphene and defective hexagonal boron nitride, and compare our predicted Raman response to experimental results, with good agreement. Our method opens up many possibilities for future studies of Raman response in solid-state physics.

cond-mat.mtrl-sci↗

arXiv2024

An upper bound on the per-tile entropy of ribbon tilings

This paper considers $n$-ribbon tilings of general regions and their per-tile entropy (the binary logarithm of the number of tilings divided by the number of tiles). We show that the per-tile entropy is bounded above by $\log_2 n$. This bound improves the best previously known bounds of $n-1$ for general regions, and the asymptotic upper bound of $\log_2 (en)$ for growing rectangles, due to Chen and Kargin.

math.CO↗

arXiv2024

Generative Active Learning for the Search of Small-molecule Protein Binders

Despite substantial progress in machine learning for scientific discovery in recent years, truly de novo design of small molecules which exhibit a property of interest remains a significant challenge. We introduce LambdaZero, a generative active learning approach to search for synthesizable molecules. Powered by deep reinforcement learning, LambdaZero learns to search over the vast space of molecules to discover candidates with a desired property. We apply LambdaZero with molecular docking to design novel small molecules that inhibit the enzyme soluble Epoxide Hydrolase 2 (sEH), while enforcing constraints on synthesizability and drug-likeliness. LambdaZero provides an exponential speedup in terms of the number of calls to the expensive molecular docking oracle, and LambdaZero de novo designed molecules reach docking scores that would otherwise require the virtual screening of a hundred billion molecules. Importantly, LambdaZero discovers novel scaffolds of synthesizable, drug-like inhibitors for sEH. In in vitro experimental validation, a series of ligands from a generated quinazoline-based scaffold were synthesized, and the lead inhibitor N-(4,6-di(pyrrolidin-1-yl)quinazolin-2-yl)-N-methylbenzamide (UM0152893) displayed sub-micromolar enzyme inhibition of sEH.

q-bio.BM↗

arXiv2020

Learning To Navigate The Synthetically Accessible Chemical Space Using Reinforcement Learning

Over the last decade, there has been significant progress in the field of machine learning for de novo drug design, particularly in deep generative models. However, current generative approaches exhibit a significant challenge as they do not ensure that the proposed molecular structures can be feasibly synthesized nor do they provide the synthesis routes of the proposed small molecules, thereby seriously limiting their practical applicability. In this work, we propose a novel forward synthesis framework powered by reinforcement learning (RL) for de novo drug design, Policy Gradient for Forward Synthesis (PGFS), that addresses this challenge by embedding the concept of synthetic accessibility directly into the de novo drug design system. In this setup, the agent learns to navigate through the immense synthetically accessible chemical space by subjecting commercially available small molecule building blocks to valid chemical reactions at every time step of the iterative virtual multi-step synthesis process. The proposed environment for drug discovery provides a highly challenging test-bed for RL algorithms owing to the large state space and high-dimensional continuous action space with hierarchical actions. PGFS achieves state-of-the-art performance in generating structures with high QED and penalized clogP. Moreover, we validate PGFS in an in-silico proof-of-concept associated with three HIV targets. Finally, we describe how the end-to-end training conceptualized in this study represents an important paradigm in radically expanding the synthesizable chemical space and automating the drug discovery process.

cs.LG↗

arXiv2018

PIR Array Codes with Optimal Virtual Server Rate

There has been much recent interest in Private information Retrieval (PIR) in models where a database is stored across several servers using coding techniques from distributed storage, rather than being simply replicated. In particular, a recent breakthrough result of Fazelli, Vardy and Yaakobi introduces the notion of a PIR code and a PIR array code, and uses this notion to produce efficient PIR protocols. In this paper we are interested in designing PIR array codes. We consider the case when we have $m$ servers, with each server storing a fraction $(1/s)$ of the bits of the database; here $s$ is a fixed rational number with $s > 1$. A PIR array code with the $k$-PIR property enables a $k$-server PIR protocol (with $k\leq m$) to be emulated on $m$ servers, with the overall storage requirements of the protocol being reduced. The communication complexity of a PIR protocol reduces as $k$ grows, so the virtual server rate, defined to be $k/m$, is an important parameter. We study the maximum virtual server rate of a PIR array code with the $k$-PIR property. We present upper bounds on the achievable virtual server rate, some constructions, and ideas how to obtain PIR array codes with the highest possible virtual server rate. In particular, we present constructions that asymptotically meet our upper bounds, and the exact largest virtual server rate is obtained when $1 < s \leq 2$. A $k$-PIR code (and similarly a $k$-PIR array code) is also a locally repairable code with symbol availability $k-1$. Such a code ensures $k$ parallel reads for each information symbol. So the virtual server rate is very closely related to the symbol availability of the code when used as a locally repairable code. The results of this paper are discussed also in this context, where subspace codes also have an important role.

cs.IT↗

arXiv2011

Superconductivity near lattice instability: the case of NbC$_{1-x}$N$_x$ and NbN

Using density functional theory within the local density approximation we report a study of the electron-phonon coupling in NbC$_{1-x}$N$_x$ and NbN crystals in the rocksalt structure. The Fermi surface of these systems exhibits important nesting. The associated Kohn anomaly greatly increases the electron-phonon coupling and induces a structural instability when the electronic density of states reaches a critical value. Our results reproduce the observed rise in $T_{c}$ from 11.2 K to 17.3 K as the nitrogen doping is increased in NbC$_{1-x}$N$_x$. To further understand the contribution of the structural instability to the rise of the superconducting temperature, we develop a model for the Eliashberg spectral function in which the effect of the unstable phonons is set apart. We show that this model together with the McMillan formula can reproduce the increase of $T_{c}$ near the structural phase transition.

cond-mat.supr-con↗