Hidden Translation and Translating Coset in Quantum Computing

We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in $\Z_{p}^{n}$, whenever $p$ is a fixed prime. For the induction step, we introduce the problem Translating Coset generalizing both Hidden Translation and Hidden Subgroup, and prove a powerful self-reducibility result: Translating Coset in a finite solvable group $G$ is reducible to instances of Translating Coset in $G/N$ and $N$, for appropriate normal subgroups $N$ of $G$. Our self-reducibility framework combined with Kuperberg's subexponential quantum algorithm for solving Hidden Translation in any abelian group, leads to subexponential quantum algorithms for Hidden Translation and Hidden Subgroup in any solvable group.Comment: Journal version: change of title and several minor update

Aerodynamic Analysis of Turboprop Engine Air Intake

The objective of this paper is to present CFD computation of a LET L-410 engine nacelle equipped with a Walter M-601E turboprop engine. The main purpose is to estimate the air intake fluid characteristics of different air intake geometries. The results of these computations are part of an optimisation process focused on increasing the performance and reducing the losses in the ‘engine - nacelle` system. A problem with flow separation in the input section was observed. This project is supported by Ministry of Industry and Trade of the Czech Republic

Computational Modeling of Single-Cell Migration::The Leading Role of Extracellular Matrix Fibers

Cell migration is vitally important in a wide variety of biological contexts ranging from embryonic development and wound healing to malignant diseases such as cancer. It is a very complex process that is controlled by intracellular signaling pathways as well as the cell's microenvironment. Due to its importance and complexity, it has been studied for many years in the biomedical sciences, and in the last 30 years it also received an increasing amount of interest from theoretical scientists and mathematical modelers. Here we propose a force-based, individual-based modeling framework that links single-cell migration with matrix fibers and cell-matrix interactions through contact guidance and matrix remodelling. With this approach, we can highlight the effect of the cell's environment on its migration. We investigate the influence of matrix stiffness, matrix architecture, and cell speed on migration using quantitative measures that allow us to compare the results to experiments

High rate locally-correctable and locally-testable codes with sub-polynomial query complexity

In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs and LTCs with block length $n$, constant rate (which can even be taken arbitrarily close to 1), constant relative distance, and query complexity $\exp(\tilde{O}(\sqrt{\log n}))$. Previously such codes were known to exist only with $\Omega(n^{\beta})$ query complexity (for constant $\beta > 0$), and there were several, quite different, constructions known. Our codes are based on a general distance-amplification method of Alon and Luby~\cite{AL96_codes}. We show that this method interacts well with local correctors and testers, and obtain our main results by applying it to suitably constructed LCCs and LTCs in the non-standard regime of \emph{sub-constant relative distance}. Along the way, we also construct LCCs and LTCs over large alphabets, with the same query complexity $\exp(\tilde{O}(\sqrt{\log n}))$, which additionally have the property of approaching the Singleton bound: they have almost the best-possible relationship between their rate and distance. This has the surprising consequence that asking for a large alphabet error-correcting code to further be an LCC or LTC with $\exp(\tilde{O}(\sqrt{\log n}))$ query complexity does not require any sacrifice in terms of rate and distance! Such a result was previously not known for any $o(n)$ query complexity. Our results on LCCs also immediately give locally-decodable codes (LDCs) with the same parameters

Economics and Business handbook

2002 handbook for the faculty of Economics and Busines

Interplay between motility and cell-substratum adhesion in amoeboid cells

The effective migration of amoeboid cells requires a fine regulation of cell-substratum adhesion. These entwined processes have been shown to be regulated by a host of biophysical and biochemical cues. Here, we reveal the pivotal role played by calcium-based mechanosensation in the active regulation of adhesion resulting in a high migratory adaptability. Using mechanotactically driven Dictyostelium discoideum amoebae, we uncover the existence of optimal mechanosensitive conditions—corresponding to specific levels of extracellular calcium—for persistent directional migration over physicochemically different substrates. When these optimal mechanosensitive conditions are met, noticeable enhancement in cell migration directionality and speed is achieved, yet with significant differences among the different substrates. In the same narrow range of calcium concentrations that yields optimal cellular mechanosensory activity, we uncovered an absolute minimum in cell-substratum adhesion activity, for all considered substrates, with differences in adhesion strength among them amplified. The blocking of the mechanosensitive ion channels with gadolinium—i.e., the inhibition of the primary mechanosensory apparatus—hampers the active reduction in substrate adhesion, thereby leading to the same undifferentiated and drastically reduced directed migratory response. The adaptive behavioral responses of Dictyostelium cells sensitive to substrates with varying physicochemical properties suggest the possibility of novel surface analyses based on the mechanobiological ability of mechanosensitive and guidable cells to probe substrates at the nanometer-to-micrometer level.SUTD-MIT International Design Centre (IDC) (IDG31400104

Undifferentiated human mesenchymal stem cells (hMSCs) are highly sensitive to mechanical strain: transcriptionally controlled early osteo-chondrogenic response in vitro

SummaryObjectivePhysical cues play a crucial role in skeletogenesis and osteochondral regeneration. Although human mesenchymal stem cells (hMSCs) offer considerable therapeutic potential, little is known about the molecular mechanisms that control their differentiation. We hypothesized that mechanical strain might be an inherent stimulus for chondrogenic and/or osteogenic differentiation in undifferentiated hMSCs, where c-Fos (FOS) might play a major role in mechanotransduction.MethodhMSCs from 10 donors were intermittently stimulated by cyclic tensile strain (CTS) at 3000 μstrain for a period of 3 days. Differential gene expression of strained and unstrained hMSCs was analysed by real-time RT-PCR for several marker genes, including the transcription factors FOS, RUNX2, SOX9, and others. Additionally, alkaline phosphatase activity (ALP) was determined kinetically.ResultsThe application of CTS significantly stimulated the expression levels of the early chondrogenic and osteogenic marker genes (SOX9, LUM, DCN; RUNX2, SPARC, SPP1, ALPL); this was accompanied by stimulation of ALP activity (+38%±12 standard error of mean, P<0.05). Matrix analysis revealed that the osteo-chondrogenic response followed a coordinated expression pattern, in which FOS was attributed to early osteogenic but not chondrogenic differentiation.ConclusionUndifferentiated hMSCs are highly sensitive to mechanical strain with a transcriptionally controlled osteo-chondrogenic differentiation response in vitro

The Optimal Single Copy Measurement for the Hidden Subgroup Problem

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup problem. Previous work has identified the optimal single copy measurement for the hidden subgroup problem over abelian groups as well as for the non-abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single copy measurement for the hidden subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single copy optimal measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe

An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of size p3 and exponent p. Exploiting certain nice automorphisms of the extraspecial groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealt with directly.Comment: 10 page