Towards an optimal swap gate

We present a novel approach that generalizes the well known quantum SWAP gate to higher dimensions and construct a regular quantum gate composed entirely in terms of the generalized CNOT gate that cyclically permutes the states of d qudits for d prime. We also investigate the case for d other than prime. A key feature of the construction design relates to the periodicity evaluation for a family of linear recurrences which we achieve by exploiting generating functions and their factorization over the complex reals

Quantum Sign Permutation Polytopes

Convex polytopes are convex hulls of point sets in the $n$-dimensional space \E^n that generalize 2-dimensional convex polygons and 3-dimensional convex polyhedra. We concentrate on the class of $n$-dimensional polytopes in \E^n called sign permutation polytopes. We characterize sign permutation polytopes before relating their construction to constructions over the space of quantum density matrices. Finally, we consider the problem of state identification and show how sign permutation polytopes may be useful in addressing issues of robustness

Санитарно-эпидемиологическая экспертиза импортной пищевой продукции и продовольственного сырья как составляющая профилактического направления транспортной медицины

Санітарно епідеміологічна експертиза імпортної харчової продукції й продовольчої сировини (далі експертиза) є одним з пріоритетних напрямів діяльності транспортних підрозділів санепідслужби. Здійснюючи функцію по контролю, виявленню та попередженню впливу небезпечних факторів, пов’язаних з перевезенням вантажів, вона є однією зі складових частин профілактичного напряму транспортної медицини. Експертиза імпортованої продукції харчового призначення нерозривно пов’язана та базується на загальних принципах всієї державної політики у сфері безпеки харчової продукції та продовольчої сировини. Основою для проведення усього комплексу робіт санітарно епідеміологічного направлення є нормативна база, яка була сформована в нашій країні кілька десятиліть назад. Механізм визначення безпеки продукції та ті критерії оцінки, які були закладені в її основі, вимагають перегляду у відповідності з вимогами сьогодення та враховуючи розвиток міжнародних відносин. Зроблені деякі кроки у цьому напрямку. Наприклад, визначення експертизи у законі «Про внесення змін до закону України «Про якість та безпеку харчових продуктів та продовольчої сировини» поряд зі встановленням відповідності продукції нормативним вимогам передбачає оцінку ризику дії шкідливих факторів у процесі обігу харчових продуктів, що відповідає сучас ним вимогам до вирішення задач профілактичного напрямку, запобігання шкідливого впливу факторів, керування санітарно-епідеміологічною ситуацією взагалі та на етапі транспортування харчових грузів зокрема. Такий підхід потрібно враховувати при подальшому необхідному перегляді та формуванні нової нормативної бази.Sanіtarу epidemiological examination of imported foodstuffs and edible raw materials (then «examination») is one of the priority directions of transport sanіtarу epidemiological servise. Examination controls, discovers and prevents an influence of dangerous factors while in transportation of loads. So it’s one of the component of the transport medicine preventive activity. Examination of import foodstuffs and edible raw materials inseparably linked with and based on general principles of the food safety state policy. The foundation of the sanitary service work is the normative base, that was formed in our country about twenty years ago. It is necessary to review the mechanism of the food safety determination and its criteria in accordance with requirements of present day time and with account of the development of the international relations. One of taken steps in this direction is a characteristic of examination in law «About contributing the modification to law of the Ukraine «About quality and safety of foodstuffs and foodraw materials» where along with determination of the products correspondence to the normative requirements is provided forrisk assessment of the harmful factors in process of the turn of the food stuffs. Such approach corresponds with modern requests to decision of the prophylactic problems, prevention bad influence dangerous factors, management sanіtarу epidemiological situation in general and in step of transportation food cargo in particular. And it should be taken into account during the further necessary process of revision and forming the new normative base

A finite difference method for pricing European and American options under a geometric Lévy process

In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process

Cryopreservation of human cancers conserves tumour heterogeneity for single-cell multi-omics analysis

Background: High throughput single-cell RNA sequencing (scRNA-Seq) has emerged as a powerful tool for exploring cellular heterogeneity among complex human cancers. scRNA-Seq studies using fresh human surgical tissue are logistically difficult, preclude histopathological triage of samples, and limit the ability to perform batch processing. This hindrance can often introduce technical biases when integrating patient datasets and increase experimental costs. Although tissue preservation methods have been previously explored to address such issues, it is yet to be examined on complex human tissues, such as solid cancers and on high throughput scRNA-Seq platforms. Methods: Using the Chromium 10X platform, we sequenced a total of ~ 120,000 cells from fresh and cryopreserved replicates across three primary breast cancers, two primary prostate cancers and a cutaneous melanoma. We performed detailed analyses between cells from each condition to assess the effects of cryopreservation on cellular heterogeneity, cell quality, clustering and the identification of gene ontologies. In addition, we performed single-cell immunophenotyping using CITE-Seq on a single breast cancer sample cryopreserved as solid tissue fragments. Results: Tumour heterogeneity identified from fresh tissues was largely conserved in cryopreserved replicates. We show that sequencing of single cells prepared from cryopreserved tissue fragments or from cryopreserved cell suspensions is comparable to sequenced cells prepared from fresh tissue, with cryopreserved cell suspensions displaying higher correlations with fresh tissue in gene expression. We showed that cryopreservation had minimal impacts on the results of downstream analyses such as biological pathway enrichment. For some tumours, cryopreservation modestly increased cell stress signatures compared to freshly analysed tissue. Further, we demonstrate the advantage of cryopreserving whole-cells for detecting cell-surface proteins using CITE-Seq, which is impossible using other preservation methods such as single nuclei-sequencing. Conclusions: We show that the viable cryopreservation of human cancers provides high-quality single-cells for multiomics analysis. Our study guides new experimental designs for tissue biobanking for future clinical single-cell RNA sequencing studies

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types