Towards A Theory Of Quantum Computability

We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum Turing machine. The class of quantum computable functions is recursively enumerable, thus opening the door to a quantum computability theory which may follow some of the classical developments

Quantum Turing Machines Computations and Measurements

Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example being the intrinsic infinite nature of any quantum computation. In this paper we propose a definition of QTM, which extends and unifies the notions of Deutsch and Bernstein and Vazirani. In particular, we allow both arbitrary quantum input, and meaningful superpositions of computations, where some of them are "terminated" with an "output", while others are not. For some infinite computations an "output" is obtained as a limit of finite portions of the computation. We propose a natural and robust observation protocol for our QTMs, that does not modify the probability of the possible outcomes of the machines. Finally, we use QTMs to define a class of quantum computable functions---any such function is a mapping from a general quantum state to a probability distribution of natural numbers. We expect that our class of functions, when restricted to classical input-output, will be not different from the set of the recursive functions.Comment: arXiv admin note: substantial text overlap with arXiv:1504.02817 To appear on MDPI Applied Sciences, 202

Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers

The first problem addressed by this article is the enumeration of some families of pattern-avoiding inversion sequences. We solve some enumerative conjectures left open by the foundational work on the topics by Corteel et al., some of these being also solved independently by Lin, and Kim and Lin. The strength of our approach is its robustness: we enumerate four families $F_1 \subset F_2 \subset F_3 \subset F_4$ of pattern-avoiding inversion sequences ordered by inclusion using the same approach. More precisely, we provide a generating tree (with associated succession rule) for each family $F_i$ which generalizes the one for the family $F_{i-1}$. The second topic of the paper is the enumeration of a fifth family $F_5$ of pattern-avoiding inversion sequences (containing $F_4$). This enumeration is also solved \emph{via} a succession rule, which however does not generalize the one for $F_4$. The associated enumeration sequence, which we call the \emph{powered Catalan numbers}, is quite intriguing, and further investigated. We provide two different succession rules for it, denoted $\Omega_{pCat}$ and $\Omega_{steady}$, and show that they define two types of families enumerated by powered Catalan numbers. Among such families, we introduce the \emph{steady paths}, which are naturally associated with $\Omega_{steady}$. They allow us to bridge the gap between the two types of families enumerated by powered Catalan numbers: indeed, we provide a size-preserving bijection between steady paths and valley-marked Dyck paths (which are naturally associated with $\Omega_{pCat}$). Along the way, we provide several nice connections to families of permutations defined by the avoidance of vincular patterns, and some enumerative conjectures.Comment: V2 includes modifications suggested by referees (in particular, a much shorter Section 3, to account for arXiv:1706.07213

Slicings of parallelogram polyominoes, or how Baxter and Schröder can be reconciled

We provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schröder and Baxter generalizations of parallelogram polyominoes (called slicings) which grow according to these succession rules. We also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset of triples of non-intersecting lattice paths, and a new Schröder subset of Baxter permutations

Antimicrobial activity of supramolecular salts of gallium(III) and proflavine and the intriguing case of a trioxalate complex

The use of the gallium oxalate complex [Ga(ox)(3)](3-) as a building block in the formation of a drug-drug salt with the antimicrobial agent proflavine (PF) as its proflavinium cation (HPF+), namely [HPF](3)[Ga(ox)(3)]center dot 4H(2)O, is reported together with the preparation of the potassium salt K-3[Ga(ox)(3)] and the novel dimeric gallium(III) salt K-4[Ga-2(ox)(4)(mu-OH)(2)]center dot 2H(2)O. All compounds have been characterized by solid state methods, and their performance as antimicrobial agents has been evaluated by disk diffusion assay against the bacteria strains Pseudomonas aeruginosa ATCC27853, Staphylococcus aureus ATCC25923, and Escherichia coli ATCC25922. While the [HPF](3)[Ga(ox)(3)]center dot 4H(2)O drug-drug salt is effective against all three strains, the gallium oxalate salt K-3[Ga(ox)(3)] showed impressive selectivity towards P. aeruginosa, with little to no antimicrobial activity against the other two organisms. This work presents novel breakthroughs towards Ga based antimicrobial agents

Wheat Grain Composition, Dough Rheology and Bread Quality as Affected by Nitrogen and Sulfur Fertilization and Seeding Density

Flour from old varieties are usually considered very weak flours, and thus difficult to use in breadmaking especially when processed as Italian \u201cTipo 2\u201d flour. Hence, the aim of our study was to understand if agronomic treatments can be used to improve flour processability and the quality of three old wheat varieties. An experimental strip-plot scheme was used: three old wheat varieties (Andriolo, Sieve, Verna), two seeding densities, three levels of nitrogen fertilization (N35, N80, and N135), and two levels of foliar sulfur fertilization. Analyzed parameters related to kernel composition, dough rheology and bread quality. Sulfur and nitrogen treatments significantly affected protein composition and dough alveograph strength, which increased by about 34% with nitrogen fertilization, and by about 14% with the sulfur treatment. However, only nitrogen fertilization affected bread characteristics. Crumb density significantly decreased from N35 to N135, while springiness and cohesiveness increased. On the other hand, sulfur did not improve breads. This highlight the importance of performing breadmaking tests in addition to the rheological determinations. The poor technological performance of old wheat flours can be improved with agronomical treatments designed to obtain higher-quality bread

Natural stone masonry characterization for the shaking-table test of a scaled building specimen

This paper discusses the material characterization tests on stone masonry specimens, and the in-plane cyclic shear-compression tests on four half-scale unreinforced stone masonry piers, which complement a shaking-table test on a half-scale building aggregate prototype. Material characterization tests allowed defining a mortar composition suitable for satisfying the similitude relationships associated with the half-scale tests. Vertical and diagonal compression tests provided a complete description of the mechanical properties of masonry assemblies, while in-plane cyclic shear-compression tests allow determining the hysteretic behavior of masonry piers with different aspect ratios and axial compression levels. Strength and displacement capacities corresponding to the observed damage mechanisms and failure modes were also identified and associated with the specimens geometric and loading conditions. These activities are part of an experimental and numerical research project jointly carried by the University of Pavia, Italy, and the École Polytechnique Fédérale de Lausanne, Switzerland, which aims at assessing the seismic vulnerability of natural stone masonry building aggregates of the historical center of Basel, Switzerland

quality and productivity considerations for laser cutting of lifepo4 and linimncoo2 battery electrodes

Abstract Laser cutting of lithium-ion battery electrodes has been shown to be a viable alternative to mechanical blanking for some specific electrode types, yielding similar cut quality and throughput but with decreased on-going costs due to lower maintenance requirements. The multitude of electrode chemistries within the lithium-ion classification, particularly with regards to the cathode, together with the sensitive nature of battery components such as the polymeric separator films and electrodes themselves, requires careful assessment of defects for each electrode type. In the present work, cutting of LiNiMnCoO2 (LNMC) coated aluminium cathodes and graphite coated copper anodes is performed at 100 mm/s with a 1064 nm pulsed fibre laser with 25 μm spot size, varying the pulse duration, energy and repetition rate over the ranges 4-200 ns, 8-935 μJ and 20-500 kHz, respectively. Process productivity is assessed in terms of the minimum cutting power at which complete electrode penetration takes place. A scanning electron microscope is utilised to assess upper coating layer clearance width and to determine the presence and dimensions of defects resulting from melting of the coating layers. Results are compared with previous cuts performed on LiFePO4 (LFP), with differences observed in the parameters leading to minimum average cutting power and optimum quality between cathode types. Laser pulse fluence in the range 35-40 J/cm2 with 30 ns pulse duration and 100 kHz repetition rate is found to lead to the highest cutting efficiency and quality for the LFP cathode, while 110-150 J/cm2 fluence with 200 ns pulse duration and 20 kHz repetition rate is instead found to be ideal for the LNMC cathode and for the anode. The present on-going study indicates relatively strong sensitivities to electrode composition and laser pulse fluence for cutting efficiency and quality

PRDI-BF1 and PRDI-BF1P isoform expressions correlate with disease status in multiple myeloma patients

Human positive regulatory domain I binding factor 1 (PRDI-BF1 or BLIMP-1) is a transcription factor that acts as a master regulator and has crucial roles in the control of differentiation and in maintaining survival of plasma cells (PC). The PRDM1 gene, which codifies for PRDI-BF1, contains an alternative promoter capable of generating a PRDI-BF1 deleted protein (called PRDI-BF1β), which lacks 101 amino acids comprising most of the regulatory domain. PRDI-BF1β has been detected in relevant quantities especially in multiple myeloma cell lines (U266 and NCI- H929). The first aim of the study was to compare, using real time polymerase chain reaction (RT-PCR), the levels of PRDI-BF1 and PRDI-BF1β in myeloma patients and in normal human bone marrow. The second step was the examination of the expression of PRDI-BF1 and PRDI-BF1β isoform depending on disease status and treatment response. We demonstrate the correlation of PRDI-BF1 and the shorter PRDI-BF1β isoform protein levels with the clinical evolution and the management of myeloma patients