A Homological Approach to Factorization

Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated localizations of D and projections onto partially ordered quotient groups of G(D). We use this functor to construct many cochain complexes of o-homomorphisms of po-groups. These complexes naturally lead to some fundamental structure theorems and some natural homology theory that provide insight into the factorization behavior of D.Comment: Submitted for publication 12/15/201

Assessing Non-Atomicity in Groups of Divisibility

An integral domain D is atomic if every non-zero non-unit is a product of irreducibles. More generally, D is quasi-atomic if every non-zero non-unit divides some product of atoms. Arbitrary integral domains, however, cannot be assumed to be quasi-atomic in general; factorization in a non-atomic D can be subtle. We outline a novel method of qualifying the quasi-atomicity of D by studying ascending filtrations of localizations of D and the associated groups of divisibility. This approach yields structure theorems, cochain complexes, and cohomological results. We take care to present examples of integral domains exhibiting the spectrum of factorization behavior and we relate the results of our new method to factorization in D

Assessing Non-Atomicity in Groups of Divisibility

An integral domain D is atomic if every non-zero non-unit is a product of irreducibles. More generally, D is quasi-atomic if every non-zero non-unit divides some product of atoms. Arbitrary integral domains, however, cannot be assumed to be quasi-atomic in general; factorization in a non-atomic D can be subtle. We outline a novel method of qualifying the quasi-atomicity of D by studying ascending filtrations of localizations of D and the associated groups of divisibility. This approach yields structure theorems, cochain complexes, and cohomological results. We take care to present examples of integral domains exhibiting the spectrum of factorization behavior and we relate the results of our new method to factorization in D

Fusion One-Time Non-Interactively-Aggregatable Digital Signatures From Lattices

We present Fusion, a post-quantum one-time digital signature scheme with non-interactive aggregation with security resting on the short integer solution problem over ideal lattices. Fusion is structurally similar to CRYSTALS-Dilithium, but Fusion is based upon the aggregatable one-time lattice-based scheme by Boneh and Kim. Fusion parameters conservatively target at least $128$ bits of security against forgery, taking tightness gaps into account, and with tighter bounds than the BK scheme. Aggregate Fusion signatures are logarithmically sized in the number of keys, so aggregating enough signatures can be more efficient than stacking Dilithium or Falcon signatures

Thring Signatures and their Applications to Spender-Ambiguous Digital Currencies

We present threshold ring multi-signatures (thring signatures) for collaborative computation of ring signatures. We discuss a game of existential forgery for thring signatures and the uses of thring signatures in digital currencies, including spender-ambiguous cross-chain atomic swaps for confidential amounts without a trusted set-up. We present an implementation of thring signatures inspired by the works of [13], [20], [14], [1], [18], and [15] we call linkable spontaneous threshold anonymous group (LSTAG) signatures, and we prove the implementation existentially unforgeable under the plain public key and random oracle models

Concise Linkable Ring Signatures and Forgery Against Adversarial Keys

We demonstrate that a version of non-slanderability is a natural definition of unforgeability for linkable ring signatures. We present a linkable ring signature construction with concise signatures and multi-dimensional keys that is linkably anonymous if a variation of the decisional Diffie-Hellman problem with random oracles is hard, linkable if key aggregation is a one-way function, and non-slanderable if a one-more variation of the discrete logarithm problem is hard. We remark on some applications in signer-ambiguous confidential transaction models without trusted setup

Transmission Shifts Underlie Variability in Population Responses to Yersinia pestis Infection

Host populations for the plague bacterium, Yersinia pestis, are highly variable in their response to plague ranging from near deterministic extinction (i.e., epizootic dynamics) to a low probability of extinction despite persistent infection (i.e., enzootic dynamics). Much of the work to understand this variability has focused on specific host characteristics, such as population size and resistance, and their role in determining plague dynamics. Here, however, we advance the idea that the relative importance of alternative transmission routes may vary causing shifts from epizootic to enzootic dynamics. We present a model that incorporates host and flea ecology with multiple transmission hypotheses to study how transmission shifts determine population responses to plague. Our results suggest enzootic persistence relies on infection of an off-host flea reservoir and epizootics rely on transiently maintained flea infection loads through repeated infectious feeds by fleas. In either case, early-phase transmission by fleas (i.e., transmission immediately following an infected blood meal) has been observed in laboratory studies, and we show that it is capable of driving plague dynamics at the population level. Sensitivity analysis of model parameters revealed that host characteristics (e.g., population size and resistance) vary in importance depending on transmission dynamics, suggesting that host ecology may scale differently through different transmission routes enabling prediction of population responses in a more robust way than using either host characteristics or transmission shifts alone

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Search for supersymmetry in events with one lepton and multiple jets in proton-proton collisions at root s=13 TeV

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