Distinct Permutations Research Articles

The effect of hydrogen co-injection on the microstructure of triple ion irradiated F82H

The reduced activation ferritic/martensitic steel F82H-IEA was studied through a systematic set of dual (Fe2++He2+) and triple (Fe2++He2++H+) ion irradiations to determine the effect of hydrogen co-injection with helium and radiation damage on the irradiated microstructure and in particular, cavity evolution. Irradiations were conducted in four distinct permutations from a set of nominal irradiation parameters of 50 dpa, 1 × 10–3 dpa/s, 500 °C, and 40/10 appm/dpa of H/He or 10 appm/dpa of He. A temperature series of dual and triple ions ranging from 400 to 600 °C was conducted where swelling values of 1.3–2.4x were obtained with the co-injection of hydrogen. A damage level (50 to 150 dpa) and damage rate (2.5 × 10–4 to 2.5 × 10–3 dpa/s) series were also conducted where hydrogen was again observed to cause a ∼1.2–1.8x increase in swelling in triple ion irradiation versus dual ions. The effect of hydrogen was also observed to increase the overall steady state swelling rate from 0.02%/dpa in dual ions to 0.034%/dpa under triple ions at 500 °C by 150 dpa. A final series of triple ion experiments was conducted at 450 °C and 500 °C at 80 appm/dpa of H where swelling was suppressed by 50% compared to the dual ion irradiated case due to over-nucleation of small bubbles. The effect of hydrogen on bubble nucleation was to stabilize higher densities of smaller helium bubbles possibly through increasing nucleation rates and reduction of the stable bubble radius. The effect on swelling was in the promotion of higher densities of larger voids experiencing bias-driven growth. Hydrogen was shown to have a moderate influence on the nucleation and growth of dislocation loops, although these effects appear to be convoluted by the changes in cavity microstructure dominating sink strength across conditions. Hydrogen co-injection was also loosely correlated with enhanced dissolution of M23C6 precipitates across temperature and damage level regimes.

160 Gbps MMF/FSO system based on OAM beams and PV code under rainy weather

In this paper, a high-speed transmission system that combines a multimode fiber (MMF) with Free Space Optics (FSO) is proposed to accommodate the rapid growth of traffic. As Orbital Angular Beams Multiplexing (OAM) plays a crucial role in 6G networks by enhancing transmission capacity, four OAM beams (LG0,0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${LG}_{\\mathrm{0,0}}$$\\end{document}, LG0,20\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${LG}_{\\mathrm{0,20}}$$\\end{document}, LG0,40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${LG}_{\\mathrm{0,40}}$$\\end{document}, and LG0,40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${LG}_{\\mathrm{0,40}}$$\\end{document}) are utilized in this study. Additionally, the Optical Code Division Multiple Access (OCDMA) technique is employed, known for its high level of confidentiality and the ability to allow multiple channels to transmit data simultaneously. To ensure ubiquitous data transmission, two channels: MMF and FSO are used. Accordingly, in our proposed MMF/FSO system, we employ four OAM beams, with each carrying four OCDMA channels assigned distinct Permutation Vector (PV) codes. With a data transmission rate of 10 Gbps on each OCDMA channel, the overall capacity of the system amounts to 160 Gbps (10 Gbps × 4 OCDMA channels × 4 OAM beams). Moreover, the performance is investigated and evaluated using two scenarios. The first assumes an FSO range of 5 km and Clear Air (CA) weather conditions, with a variable MMF length. In contrast, the second scenario maintains a fixed MMF length of 1 km while altering the FSO span. Weather conditions like CA and rain conditions; Light Rain (LR), Medium Rain (MR), and Heavy Rain (HR) are considered while evaluating the system performance in the second case. The bit error rate (BER), travelling distances in the channel either MMF or FSO, and eye diagrams are among the metrics used for evaluation. They all provide information about the received signal performance. Finally, the obtained results for the proposed MMF/FSO system, utilizing OAM beams and PV codes, indicate that in the first scenario, the system can support a total capacity of 160 Gbps across all channels. The performance is noteworthy, with a BER below 10-5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${10}^{-5}$$\\end{document} and a wide eye opening, enabling successful transmission over 6.2 km (1.2 km MMF length + fixed 5 km FSO span). For the second scenario, the achievable distance is decreased due to the attenuation caused by rain. It becomes 2.62 km (1 km MMF + 1.62 km FSO span), 5.2 km (1 km MMF + 1.2 km FSO span), and 1.77 km (1 km MMF + 0.77 km FSO span), under LR, MR, and HR, respectively.

“Shang Chi And the Legend of The Ten Rings": Tense and Perspective

Due to English's global significance, it indirectly affects Indonesia's education system. In this area of study, most scholarly publications speak English. All Indonesian nationals are required by law to take English classes. Many students have trouble understanding the grammatical rules of English because they are so different from those of their native language, Indonesian. The most important distinctions are those of tense and aspect. Many students struggle with grammar because of this. This analysis aims to determine which tenses and aspects are used in the script for "Shang Chi and the Legend of the Ten Rings," and which are employed most often. This research makes use of content analysis and qualitative descriptive methods. Data collection made use of record-keeping. The data was examined using the Miles and Huberman dynamic model. After the data has been compiled and presented, inferences can be made. The data shows that there are nine distinct permutations of tense and aspect. There are 33 current tenses, 37 past tenses, 6 future tenses, 35 progressive tenses, 3 past progressive tenses, 3 perfect tenses, 1 perfect tenses, 2 future perfect tenses, and 2 present perfect tenses. The present progressive is only represented by 35 occurrences, while the plain past tense is represented by 37. There are twelve permutations of tense and aspect, nine of which are used here. There is no distinction between past and future occurrences in the progressive tenses (future, past, and future perfect).

Permutation symmetry in spin-adapted many-body wave functions.

In the domain of exchange-coupled polynuclear transition-metal (PNTM) clusters, local emergent symmetries exist which can be exploited to greatly increase the sparsity of the configuration interaction (CI) eigensolutions of such systems. Sparsity of the CI secular problem is revealed by exploring the site permutation space within spin-adapted many-body bases, and highly compressed wave functions may arise by finding optimal site orderings. However, the factorial cost of searching through the permutation space remains a bottleneck for clusters with a large number of metal centers. In this work, we explore ways to reduce the factorial scaling, by combining permutation and point group symmetry arguments, and using commutation relations between cumulative partial spin and the Hamiltonian operators, . Certain site orderings lead to commuting operators, from which more sparse wave functions arise. Two graphical strategies will be discussed, one to rapidly evaluate the commutators of interest, and one in the form of a tree search algorithm to predict how many and which distinct site permutations are to be analyzed, eliminating redundancies in the permutation space. Particularly interesting is the case of the singlet spin states for which an additional reversal symmetry can be utilized to further reduce the number of distinct site permutations.

Making the undetectable detectable: Pushing limits of biomolecular recognition by ultra-sensitive multiplexed single-particle liposome readouts.

Biomolecular recognition is fundamental for all biological and chemical processes. However, current screening methods are often reliant on large robotic devices, require long running times and much manpower as well as excessive materials cost. Here I will present our recent work implementing multiple miniaturized screening assays for ultra-sensitive and high-throughput readout at the single-particle level of DNA-DNA recognition, sub-attoliter cargo delivery, transporter function and label-free DNA biosensing. I will focus on the single-particle combinatorial multiplexed liposome fusion mediated by DNA for parallelized multistep and non-deterministic fusion of individual sub-attoliter nanocontainers (SPARCLD). Our new toolbox allowed us to attain efficient (>93%) and leakage free stochastic fusion sequences for arrays of surface-tethered target liposomes with six freely diffusing populations of cargo liposomes, each functionalized with individual lipidated single-stranded DNA and fluorescently barcoded by a distinct ratio of chromophores. Because each lipid nanoparticle is an autonomous nanocontainer the stochastic fusion sequence resulted in massive number of distinct permutations of cargo delivery loadings and sequences. Real-time recordings and machine learning analysis allowed the rapid classification of >16,000 fusions and 566 distinct fusion sequences within hours. The high-density arrays of surface-tethered target nanocontainers (∼42,000 containers per mm2) offers entire combinatorial multiplex screens using only picograms of material and is implanted for screening transporter function and label free DNA biosensing.

Single-particle combinatorial multiplexed liposome fusion mediated by DNA.

Combinatorial high-throughput methodologies are central for both screening and discovery in synthetic biochemistry and biomedical sciences. They are, however, often reliant on large-scale analyses and thus limited by a long running time and excessive materials cost. We here present a single-particle combinatorial multiplexed liposome fusion mediated by DNA for parallelized multistep and non-deterministic fusion of individual subattolitre nanocontainers. We observed directly the efficient (>93%) and leakage free stochastic fusion sequences for arrays of surface-tethered target liposomes with six freely diffusing populations of cargo liposomes, each functionalized with individual lipidated single-stranded DNA and fluorescently barcoded by a distinct ratio of chromophores. The stochastic fusion resulted in a distinct permutation of fusion sequences for each autonomous nanocontainer. Real-time total internal reflection imaging allowed the direct observation of >16,000 fusions and 566 distinct fusion sequences accurately classified using machine learning. The high-density arrays of surface-tethered target nanocontainers (~42,000 containers per mm2) offers entire combinatorial multiplex screens using only picograms of material.

Power permutation modulation in multiple‐input multiple‐output systems

AbstractThe forthcoming communications standards are conjectured to require unprecedentedly high spectral efficiency values. Motivated by this fact, we propose a new transmission scheme for multiple‐input multiple‐output systems, which is termed as power permutation modulation (PPM). In addition to the conventional data‐carrying modulated symbols, some amount of extra information is conveyed in the distinct permutations of power allocation levels associated with the modulated symbols. The detection of the additional bits is performed by a power permutation recovery process at the receive side. Unlike the common approach, the power allocation is exploited as a new degree of freedom for carrying information without requiring any channel state information at the transmitter. The application of the introduced method is exemplified for zero‐forcing beamforming and space‐time block coding systems under digital phase modulation. It is shown that, without any important additional complexity, some notable signal‐to‐noise ratio gains (as large as 3 dB) are attained as compared to the standard approaches. An exact closed‐form result on the bit error rate (BER) of the presented PPM scheme is provided. The obtained expression is used to obtain the optimum power allocation levels such that the overall BER is minimized.

Packing of permutations into Latin squares

For every positive integer n greater than 4 there is a set of Latin squares of order n such that every permutation of the numbers 1,…,n appears exactly once as a row, a column, a reverse row or a reverse column of one of the given Latin squares. If n is greater than 4 and not of the form p or 2p for some prime number p congruent to 3 modulo 4, then there always exists a Latin square of order n in which the rows, columns, reverse rows and reverse columns are all distinct permutations of 1,…,n, and which constitute a permutation group of order 4n. If n is prime congruent to 1 modulo 4, then a set of (n−1)∕4 mutually orthogonal Latin squares of order n can also be constructed by a classical method of linear algebra in such a way, that the rows, columns, reverse rows and reverse columns are all distinct and constitute a permutation group of order n(n−1).

Oriented diameter of star graphs

An orientation of an undirected graph G is an assignment of exactly one direction to each edge of G . Converting two-way traffic networks to one-way traffic networks and bidirectional communication networks to unidirectional communication networks are practical instances of graph orientations. In these contexts minimising the diameter of the resulting oriented graph is of prime interest. The n -star network topology was proposed as an alternative to the hypercube network topology for multiprocessor systems by Akers and Krishnamurthy (1989). The n -star graph S n consists of n ! vertices, each labelled with a distinct permutation of [ n ] . Two vertices are adjacent if their labels differ exactly in the first and one other position. S n is an ( n − 1 ) -regular, vertex-transitive graph with diameter ⌊ 3 ( n − 1 ) / 2 ⌋ . Orientations of S n , called unidirectional star graphs and distributed routing protocols over them were studied by Day and Tripathi (1993) and Fujita (2013). Fujita showed that the (directed) diameter of this unidirectional star graph S n ⃗ is at most ⌈ 5 n / 2 ⌉ + 2 . In this paper, we propose a new distributed routing algorithm for the same S n ⃗ analysed by Fujita, which routes a packet from any node s to any node t at an undirected distance d from s using at most min { 4 d + 4 , 2 n + 4 } hops. This shows that the (directed) diameter of S n ⃗ is at most 2 n + 4 . We also show that the diameter of S n ⃗ is at least 2 n when n ≥ 7 , thereby showing that our upper bound is tight up to an additive factor.

Label-free single-molecule identification of telomere G-quadruplexes with a solid-state nanopore sensor.

Telomere sequences can spontaneously form G-quadruplexes (G4) in the presence of some cations. In view of their relevance to genetic processes and potential as therapeutic-targets, hitherto, a wealth of conventional techniques have been reported for interrogation of G4 conformation diversity and corresponding folding kinetics, most of which are limited in precision and sensitivity. This work introduces a label-free solid-state nanopore (SSN) approach for the determination of inter-, intra- and tandem molecular G4 with distinct base permutation in various cation buffers with a tailored aperture and meanwhile captures the single-molecule G4 folding process. SSN translocation properties elucidated that both inter- and intramolecular G4 generated higher current blockage with longer duration than flexible homopolymer nucleotide, and intramolecular G4 are structurally more stable with higher event frequency and longer blockage time than intermolecular ones; base arrangement played weak role in translocation behaviors; the same sequences with one, two and three G4 skeletons displayed an increase in current blockage and a gradual extension in dwell time with the increase of molecule size recorded in the same nanopore. We observed the conformation change of single-molecule G4 which indicated the existence of folding/unfolding equilibration in nanopore, and real-time test suggested a gradual formation of G4 with time. Our results could provide a continued and improved understanding of the underlying relevance of structural stability and G4 folding process by utilizing SSN platform which exhibits strategic potential advances over the other methods with high spatial and temporal resolution.

A Permutation Test for Comparing Two Correlated Receiver Operating Characteristic Curves

The area under the Receiver Operating Characteristic (ROC) curve (AUC) is a summary measure when comparing two ROC curves. However, this summary measure is less informative when two ROC curves cross and have the same AUCs. In order to detect differences between ROC curves and to be able to tackle the problem of exchangeability of the labels between two diagnostic tests within subject, an alternative permutation test based on between-subject permutations of the labels of the subjects within each diagnostic test is proposed for assessing a change in the AUCs in a continuous matched pair of data from two diagnostic test procedures having both non-diseased and diseased subject in each of the test. The Wilcoxon signed rank test statistic was modified as a permutation test under the null hypothesis of equality of AUCs. An algorithm for carrying out complete enumeration of all the distinct permutations of the paired test results was developed which provides exact p-values. Using simulated data, the proposed test compares in statistical power to the modified sign test proposed by Braun and Alonzo but the proposed test has better operating characteristics, that is greater statistical power to detect a crossing alternative and is less conservative in test size and in the range of parameters of at least 0.8 of AUCs on the average with a correlation of at least 0.4 and small to moderately large sample sizes. Similarly in applying real life data, the proposed test has the more likelihood of rejecting null hypothesis of equality of AUC1 and AUC2 at nominal level of 0.05 with the proposed test having a p-value of 0.0312 against the Braun and Alonzo’s test with a p-value of 0.0387. This is because the proposed test is modified to adjust for the presence of zero differences in values and considers the signs of values as well as the absolute ranks of values. Also the estimates of AUC1 and AUC2 for the two diagnostic tests are 0.668 and 0.887 respectively showing that AUC2, that is 2hour 100g Oral Glucose Tolerance Test (OGTT) is superior to AUC1 (2hour 70g OGTT) at a time that the specificity is greater than 0.7.

Drug-target prediction utilizing heterogeneous bio-linked network embeddings.

To enable modularization for network-based prediction, we conducted a review of known methods conducting the various subtasks corresponding to the creation of a drug-target prediction framework and associated benchmarking to determine the highest-performing approaches. Accordingly, our contributions are as follows: (i) from a network perspective, we benchmarked the association-mining performance of 32 distinct subnetwork permutations, arranging based on a comprehensive heterogeneous biomedical network derived from 12 repositories; (ii) from a methodological perspective, we identified the best prediction strategy based on a review of combinations of the components with off-the-shelf classification, inference methods and graph embedding methods. Our benchmarking strategy consisted of two series of experiments, totaling six distinct tasks from the two perspectives, to determine the best prediction. We demonstrated that the proposed method outperformed the existing network-based methods as well as how combinatorial networks and methodologies can influence the prediction. In addition, we conducted disease-specific prediction tasks for 20 distinct diseases and showed the reliability of the strategy in predicting 75 novel drug-target associations as shown by a validation utilizing DrugBank 5.1.0. In particular, we revealed a connection of the network topology with the biological explanations for predicting the diseases, 'Asthma' 'Hypertension', and 'Dementia'. The results of our benchmarking produced knowledge on a network-based prediction framework with the modularization of the feature selection and association prediction, which can be easily adapted and extended to other feature sources or machine learning algorithms as well as a performed baseline to comprehensively evaluate the utility of incorporating varying data sources.

Enhanced Receiver Based on FEC Code Constraints for Uplink NOMA With Imperfect CSI

Non-orthogonal multiple access (NOMA) has been envisioned as a useful component of fifth generation (5G) mobile networks. As imperfect channel state information (CSI) due to channel estimation errors poses problems for most wireless receivers, it presents even greater challenges in successive interference cancellation (SIC) reception of NOMA signals. We present a novel approach to the multi-user detection problem by exploiting the important constraints of forward error correction (FEC) code word. We devise our new receiver based on the minimum output energy (MOE) criterion while preserving a distortionless response to the user equipment (UE) of interest. In particular, we efficiently adopt the UE signatures presented by the FEC channel codes under distinct permutations to separate desired signals of interest from interfering UEs. We formulate our receiver optimization into a quadratic-programming problem anchored with a set of code constraints. Our simulations demonstrate that the proposed code-anchored quadratic programming (CQP) receiver can accurately improve SIC performance and provide robustness to CSI errors better than other legacy schemes.

New lower bounds for permutation arrays using contraction

A permutation array A is a set of permutations on a finite set $$\Omega $$ , say of size n. Given distinct permutations $$\pi , \sigma \in \Omega $$ , we let $$hd(\pi , \sigma ) = |\{ x\in \Omega : \pi (x) \ne \sigma (x) \}|$$ , called the Hamming distance between $$\pi $$ and $$\sigma $$ . Now let $$hd(A) =$$ min $$\{ hd(\pi , \sigma ): \pi , \sigma \in A \}$$ . For positive integers n and d with $$d\le n$$ we let M(n, d) be the maximum number of permutations in any array A satisfying $$hd(A) \ge d$$ . There is an extensive literature on the function M(n, d), motivated in part by suggested applications to error correcting codes for message transmission over power lines. A basic fact is that if a permutation group G is sharply k-transitive on a set of size $$n\ge k$$ , then $$M(n,n-k+1) = |G|$$ . Motivated by this we consider the permutation groups AGL(1, q) and PGL(2, q) acting sharply 2-transitively on GF(q) and sharply 3-transitively on $$GF(q)\cup \{\infty \}$$ respectively. Applying a contraction operation to these groups, we obtain the following new lower bounds for prime powers q satisfying $$q\equiv 1$$ (mod 3). These results resolve a case left open in a previous paper (Bereg et al. in Des Codes Cryptogr 86(5):1095–1111, 2018), where it was shown that $$M(q-1, q-3) \ge q^{2} - q$$ and $$M(q,q-3) \ge q^{3} - q$$ for all prime powers q such that $$q\not \equiv 1$$ (mod 3). We also obtain lower bounds for M(n, d) for a finite number of exceptional pairs n, d, by applying this contraction operation to the sharply 4 and 5-transitive Mathieu groups.

On the rank of a Latin tensor

An n×n matrix A is called permutative if the rows of A are distinct permutations of a family of n distinct elements. For all n⩾3, we show that the minimal rank of a non-negative permutative matrix equals 3. The minimal rank of a generic permutative n×n matrix equals the smallest integer r such that r!⩾n. Our results answer the questions asked recently by Hu, Johnson, Davis, Zhang, and we show how to generalize them to tensors.

Permutation glass.

The field of disordered systems in statistical physics provides many simple models in which the competing influences of thermal and nonthermal disorder lead to new phases and nontrivial thermal behavior of order parameters. In this paper, we add a model to the subject by considering a disordered system where the state space consists of various orderings of a list. As in spin glasses, the disorder of such "permutation glasses" arises from a parameter in the Hamiltonian being drawn from a distribution of possible values, thus allowing nominally "incorrect orderings" to have lower energies than "correct orderings" in the space of permutations. We analyze a Gaussian, uniform, and symmetric Bernoulli distribution of energy costs, and, by employing Jensen's inequality, derive a simple condition requiring the permutation glass to always transition to the correctly ordered state at a temperature lower than that of the nondisordered system, provided that this correctly ordered state is accessible. We in turn find that in order for the correctly ordered state to be accessible, the probability that an incorrectly ordered component is energetically favored must be less than the inverse of the number of components in the system. We show that all of these results are consistent with a replica symmetric ansatz of the system. We conclude by arguing that there is no distinct permutation glass phase for the simplest model considered here and by discussing how to extend the analysis to more complex Hamiltonians capable of novel phase behavior and replica symmetry breaking. Finally, we outline an apparent correspondence between the presented system and a discrete-energy-level fermion gas. In all, the investigation introduces a class of exactly soluble models into statistical mechanics and provides a fertile ground to investigate statistical models of disorder.

Turbo Codes Performance Optimization over Block Fading Channels

In this paper, the best achievable performance of a turbo coded system on a block fading channel is obtained, assuming binary antipodal modulation. A rate 1/3 turbo code is considered, obtained by concatenating, through a random interleaver, an 8-states rate 1/2 and a rate 1 convolutional codes (CC). The block fading channel model is motivated by the fact that in many wireless systems the coherence time of the channel is much longer than one symbol interval, resulting in adjacent symbols being affected by the same fading value. The fading blocks will experience independent fades, assuming a sufficient separation in time, in frequency, or both in time and in frequency. This channel model is suitable for analyzing, forinstance, wireless communication systems employing techniques such as slow frequency-hopping, as is done in the Global System for Mobile communications (GSM).In such systems, coded information is transmitted over a small number of fading channels in order to achieve diversity. The best coded information allocations over a certain number of fading channels are evaluated, using the Eades-McKay algorithm to generate distinct permutations of a multiset. Bounds on the achievable performance due to coding are derived using information-theoretic techniques. In particular, in the paper an analytical method is proposed, based on the sphere-packing bounding technique, to assess the achievable performance. Moreover, simulation results are obtained and compared with the theoretical ones.

Astrobiology as a framework for investigating antibiotic susceptibility: a study of Halomonas hydrothermalis.

Physical and chemical boundaries for microbial multiplication on Earth are strongly influenced by interactions between environmental extremes. However, little is known about how interactions between multiple stress parameters affect the sensitivity of microorganisms to antibiotics. Here, we assessed how 12 distinct permutations of salinity, availability of an essential nutrient (iron) and atmospheric composition (aerobic or microaerobic) affect the susceptibility of a polyextremotolerant bacterium, Halomonas hydrothermalis, to ampicillin, kanamycin and ofloxacin. While salinity had a significant impact on sensitivity to all three antibiotics (as shown by turbidimetric analyses), the nature of this impact was modified by iron availability and the ambient gas composition, with differing effects observed for each compound. These two parameters were found to be of particular importance when considered in combination and, in the case of ampicillin, had a stronger combined influence on antibiotic tolerance than salinity. Our data show how investigating microbial responses to multiple extremes, which are more representative of natural habitats than single extremes, can improve our understanding of the effects of antimicrobial compounds and suggest how studies of habitability, motivated by the desire to map the limits of life, can be used to systematically assess the effectiveness of antibiotics.

FEC Code Anchored Robust Design of Massive MIMO Receivers

Massive multiple-input-multiple-output (MIMO) systems have been proposed to support high rate multiple access. As channel estimation in massive MIMO suffers from the well-known impairment of pilot contamination, we propose a novel approach to multi-user detection by exploiting forward error correction (FEC) code diversity. Unlike traditional approaches solely based on worst-case or probabilistic channel estimation errors, we develop a joint quadratic-programming (QP) receiver anchored with a set of FEC code constraints. Exploiting the user signatures presented by FEC channel codes of distinct permutations, our receiver can effectively recover signals from pilot-interfering users. The code-anchored robust design (CARD) method can also be applied to a chance-constrained receiver, which shows further performance gain compared with the direct integration of FEC code constraints in joint QP receiver. The effectiveness of CARD receivers is demonstrated by numerical results that establish substantial performance gain of the proposed receivers over existing robust designs. In addition, we present a distributed multi-cell processing scheme for enhanced performance via alternating direction method of multipliers.

The flavor-blind principle: A symmetrical approach to the Gatto-Sartori-Tonin relation

We perform a systematic study of the generic Gatto-Sartori-Tonin relation, $\tan^2\theta_{ij}= m_i/m_j$. This study of fermion mixing phenomena leads us to the necessary conditions that are needed in order to obtain it without any approximation. We begin by considering two Dirac fermion families. By means of the hierarchy in the masses, it is found that a sufficient and necessary condition is to have a normal matrix with $m_{11}=0$. This matrix can be decomposed into two different linearly independent contributions. The origin for such two independent contributions can be naturally explained by what we shall call the flavor-blind principle. This principle states that Yukawa couplings shall be either flavor-blind or decomposed into several sets obeying distinct permutation symmetries. In general, it is shown that the symmetry properties of the introduced set of Yukawa matrices follow for $n$ fermion families the unique sequential breaking $S_{nL}\otimes S_{nR} \rightarrow S_{(n-1)L}\otimes S_{(n-1)R} \rightarrow \cdots \rightarrow S_{2L}\otimes S_{2R} \rightarrow S_{2A}$. The particular case of three fermion families explains why the four mass ratios parametrization that we recently proposed can be used even in the case of no hierarchical masses.