Effects of topological changes in microchannel geometries on the asymmetric breakup of a droplet

Passive asymmetric breakups of a droplet could be done in many microchannels of various geometries. In order to study the effects of different geometries on the asymmetric breakup of a droplet, four types of asymmetric microchannels with the topological equivalence of geometry are designed, which are T-90, Y-120, Y-150, and I-180 microchannels. A three-dimensional volume of fluid multiphase model is employed to investigate the asymmetric rheological behaviors of a droplet numerically. Three regimes of rheological behaviors as a function of the capillary numbers Ca and the asymmetries As defined by As = (b1 ? b2)/(b1 + b2) (where b1 and b2 are the widths of two asymmetric sidearms) have been observed. A power law model based on three major factors (Ca, As and the initial volume ratio r ₀) is employed to describe the volume ratio of two daughter droplets. The analysis of pressure fields shows that the pressure gradient inside the droplet is one of the major factors causing the droplet translation during its asymmetric breakup. Besides the above similarities among various microchannels, the asymmetric breakup in them also have some slight differences as various geometries have different enhancement or constraint effects on the translation of the droplet and the cutting action of flows. It is disclosed that I-180 microchannel has the smallest critical capillary number, the shortest splitting time, and is hardest to generate satellite droplets.     

On Some Optimization Problems for the Rényi Divergence

We consider the problem of determining the maximum and minimum of the Rényi divergence D_λ(P||Q) and D_λ(Q||P) for two probability distribution P and Q of discrete random variables X and Y provided that the probability distribution P and the parameter α of α-coupling between X and Y are fixed, i.e., provided that Pr{X = Y } = α.     

Generation of droplets in the T-junction with a constriction microchannel

Droplet microfluidics plays an essential role in science and technology with various applications such as chemical engineering, environment, energy and other fields. T-junction with a constriction microchannel is designed for the controlled production of monodisperse microdroplets, which could produce droplets with the same size under a lower flow resistance. The influence of the microchannel structure, operating conditions, and physical properties on the dispersion rules is systematically investigated by combinations of micro-particle image velocimetry (Micro-PIV), high-speed camera and numerical simulation. Compared to the traditional T-junction channel, the T-junction with a constriction microchannel can generate smaller droplets whose size conforms to the size prediction formula of the traditional T-junction channel. It is found that the velocity vector of the T-junction with a constriction microchannel is faster than that in the T-junction channel at each stage of droplet generation. The droplet size is mainly based on the Ca number, the flow rate ratio and viscosity ratio of the continuous phases in our channel, and the range of the index of Ca with the droplet size is found. The constriction width has a significant influence on the dispersion rule, as there is a decreasing tendency for the droplet size with reducing constriction width.     

Observational constraints on a hyperbolic potential in brane-world inflation

We focus on the large field of a hyperbolic potential form, which is characterized by a parameter f, in the framework of the brane-world inflation in Randall-Sundrum-II model. From the observed form of the power spectrum P _R (k), the parameter f should be of order 0.1m _p to 0.001m _p , the brane tension must be in the range λ ~ (1?10)×10⁵⁷ GeV⁴, and the energy scale is around V₀ ^1/4 ~ 10¹⁵ GeV. We find that the inflationary parameters (n _s , r, and dn _s /d(ln k) depend only on the number of e-folds N. The compatibility of these parameters with the last Planck measurements is realized with large values of N.     

Engineering droplet navigation through tertiary-junction microchannels

We present an experimental and in silico investigation of path selection by a single droplet inside a tertiary-junction microchannel using oil-in-water as a model system. The droplet was generated at a T-junction inside a microfluidic chip, and its flow behavior as a function of droplet size, streamline position, viscosity, and Reynolds number (Re) of the continuous phase was studied downstream at a tertiary junction having perpendicular channels of uniform square cross section and internal fluidic resistance proportional to their lengths. Numerical studies were performed using the multicomponent lattice Boltzmann method. Both the experimental and numerical results showed good agreement and suggested that at higher Re equal to 3, the flow was dominated by inertial forces resulting in the droplets choosing a path based on their center position in the flow streamline. At lower Re of 0.3, the streamline-assisted path selection became viscous force-assisted above a critical droplet size. As the Re was further reduced to 0.03, or when the viscosity of the dispersed phase was increased, the critical droplet size for transition also decreased. This multivariate approach can in future be used to engineer sorting of cells, e.g., circulating tumor cells (CTCs) allowing early-stage detection of life-threatening diseases.     

Study of flow behaviors of droplet merging and splitting in microchannels using Micro-PIV measurement

Droplet merging and splitting are important droplet manipulations in droplet-based microfluidics. However, the fundamental flow behaviors of droplets were not systematically studied. Hence, we designed two different microstructures to achieve droplet merging and splitting respectively, and quantitatively compared different flow dynamics in different microstructures for droplet merging and splitting via micro-particle image velocimetry (micro-PIV) experiments. Some flow phenomena of droplets different from previous studies were observed during merging and splitting using a high-speed microscope. It was also found the obtained instantaneous velocity vector fields of droplets have significant influence on the droplets merging and splitting. For droplet merging, the probability of droplets coalescence (η) in a microgroove is higher (50% < η < 92%) than that in a T-junction microchannel (15% < η < 50%), and the highest coalescence efficiency (η = 92%) comes at the two-phase flow ratio e of 0.42 in the microgroove. Moreover, compared with a cylinder obstacle, Y-junction bifurcation can split droplets more effectively and the droplet flow during splitting is steadier. The results can provide better understanding of droplet behaviors and are useful for the design and applications of droplet-based microfluidics.     

On the Number of Edges of a Uniform Hypergraph with a Range of Allowed Intersections

We study the quantity p(n, k, t₁, t₂) equal to the maximum number of edges in a k-uniform hypergraph having the property that all cardinalities of pairwise intersections of edges lie in the interval [t₁, t₂]. We present previously known upper and lower bounds on this quantity and analyze their interrelations. We obtain new bounds on p(n, k, t₁, t₂) and consider their possible applications in combinatorial geometry problems. For some values of the parameters we explicitly evaluate the quantity in question. We also give a new bound on the size of a constant-weight error-correcting code.     

Bimagic Vertex Labelings

The notion of the equivalence of vertex labelings on a given graph is introduced. The equivalence of three bimagic labelings for regular graphs is proved. A particular solution is obtained for the problem of the existence of a 1-vertex bimagic vertex labeling of multipartite graphs, namely, for graphs isomorphic with K_{n, n, m}. It is proved that the sequence of bi-regular graphs K_n(ij)?=?((K_n???1???M)?+?K₁)???(u_nu_i)???(u_nu_j) admits 1-vertex bimagic vertex labeling, where u_i, u_j is any pair of non-adjacent vertices in the graph K_n???1???M, u_n is a vertex of K₁, M is perfect matching of the complete graph K_n???1. It is established that if an r-regular graph G of order n is distance magic, then graph G + G has a 1-vertex bimagic vertex labeling with magic constants (n?+?1)(n?+?r)/2?+?n² and (n?+?1)(n?+?r)/2?+?nr. Two new types of graphs that do not admit 1-vertex bimagic vertex labelings are defined.     

Sparse Support Vector Machine with <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> Penalty for Feature Selection

We study the strategies in feature selection with sparse support vector machine (SVM). Recently, the socalled L _p -SVM (0 < p < 1) has attracted much attention because it can encourage better sparsity than the widely used L ₁-SVM. However, L _p -SVM is a non-convex and non-Lipschitz optimization problem. Solving this problem numerically is challenging. In this paper, we reformulate the L _p -SVM into an optimization model with linear objective function and smooth constraints (LOSC-SVM) so that it can be solved by numerical methods for smooth constrained optimization. Our numerical experiments on artificial datasets show that LOSC-SVM (0 < p < 1) can improve the classification performance in both feature selection and classification by choosing a suitable parameter p. We also apply it to some real-life datasets and experimental results show that it is superior to L ₁-SVM.     

On finite groups with large degrees of irreducible character

Let G be a finite nontrivial group with an irreducible complex character χ of degree d = χ(1). According to the orthogonality relation, the sum of the squared degrees of irreducible characters of G is the order of G. N. Snyder proved that, if G = d(d + e), then the order of the group G is bounded in terms of e for e > 1. Y. Berkovich demonstrated that, in the case e = 1, the group G is Frobenius with the complement of order d. This paper studies a finite nontrivial group G with an irreducible complex character Θ such that G ≤ 2Θ(1)² and Θ(1) = pq where p and q are different primes. In this case, we have shown that G is a solvable group with an Abelian normal subgroup K of index pq. Using the classification of finite simple groups, we have established that the simple non-Abelian group, the order of which is divisible by the prime p and not greater than 2p ⁴ is isomorphic to one of the following groups: L ₂(q), L ₃(q), U ₃(q), S _z(8), A ₇, M ₁₁, and J ₁.     

Advanced methods for the estimation of an unknown projection from a map

This article presents three new methods (M5, M6, M7) for the estimation of an unknown map projection and its parameters. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the map projection; it could improve their georeference. The location similarity approach takes into account the residuals on the corresponding features; the minimum is found using the non-linear least squares. For the shape similarity approach, the minimized objective function ? takes into account the spatial distribution of the features, together with the shapes of the meridians, parallels and other 0D-2D elements. Due to the non-convexity and discontinuity, its global minimum is determined using the global optimization, represented by the differential evolution. The constant values of projection φ _k , λ _k , φ ₁, λ ₀, and map constants R,ΔX,ΔY, α (in relation to which the methods are invariant) are estimated. All methods are compared and the results are presented for the synthetic data as well as for 8 early maps from the Map Collection of the Charles University and the David Rumsay Map Collection. The proposed algorithms have been implemented in the new version of the detectproj software.     

Two time-efficient gibbs sampling inference algorithms for biterm topic model

Biterm Topic Model (BTM) is an effective topic model proposed to handle short texts. However, its standard gibbs sampling inference method (StdBTM) costs much more time than that (StdLDA) of Latent Dirichlet Allocation (LDA). To solve this problem we propose two time-efficient gibbs sampling inference methods, SparseBTM and ESparseBTM, for BTM by making a tradeoff between space and time consumption in this paper. The idea of SparseBTM is to reduce the computation in StdBTM by both recycling intermediate results and utilizing the sparsity of count matrix \(\mathbf {N}^{\mathbf {T}}_{\mathbf {W}}\). Theoretically, SparseBTM reduces the time complexity of StdBTM from O(|B| K) to O(|B| K _w ) which scales linearly with the sparsity of count matrix \(\mathbf {N}^{\mathbf {T}}_{\mathbf {W}}\) (K _w ) instead of the number of topics (K) (K _w < K, K _w is the average number of non-zero topics per word type in count matrix \(\mathbf {N}^{\mathbf {T}}_{\mathbf {W}}\)). Experimental results have shown that in good conditions SparseBTM is approximately 18 times faster than StdBTM. Compared with SparseBTM, ESparseBTM is a more time-efficient gibbs sampling inference method proposed based on SparseBTM. The idea of ESparseBTM is to reduce more computation by recycling more intermediate results through rearranging biterm sequence. In theory, ESparseBTM reduces the time complexity of SparseBTM from O(|B|K _w ) to O(R|B|K _w ) (0 < R < 1, R is the ratio of the number of biterm types to the number of biterms). Experimental results have shown that the percentage of the time efficiency improved by ESparseBTM on SparseBTM is between 6.4% and 39.5% according to different datasets.     

On s-uniform property of compressing sequences derived from primitive sequences modulo odd prime powers

Let Z/(p^e) be the integer residue ring modulo p^e with p an odd prime and e ≥ 2. We consider the suniform property of compressing sequences derived from primitive sequences over Z/(p^e). We give necessary and sufficient conditions for two compressing sequences to be s-uniform with α provided that the compressing map is of the form ?(x₀, x₁,...,x_e?1) = g(x_e?1) + η(x₀, x₁,..., x_e?2), where g(x_e?1) is a permutation polynomial over Z/(p) and η is an (e ? 1)-variable polynomial over Z/(p).     

Interactive Restless Multi-armed Bandit Game and Swarm Intelligence Effect

We obtain the conditions for the emergence of the swarm intelligence effect in an interactive game of restless multi-armed bandit (rMAB). A player competes with multiple agents. Each bandit has a payoff that changes with a probability p _c per round. The agents and player choose one of three options: (1) Exploit (a good bandit), (2) Innovate (asocial learning for a good bandit among n _I randomly chosen bandits), and (3) Observe (social learning for a good bandit). Each agent has two parameters (c, p _obs ) to specify the decision: (i) c, the threshold value for Exploit, and (ii) p _obs , the probability for Observe in learning. The parameters (c, p _obs ) are uniformly distributed. We determine the optimal strategies for the player using complete knowledge about the rMAB. We show whether or not social or asocial learning is more optimal in the (p _c , n _I ) space and define the swarm intelligence effect. We conduct a laboratory experiment (67 subjects) and observe the swarm intelligence effect only if (p _c , n _I ) are chosen so that social learning is far more optimal than asocial learning.     

On the Issue of the Gravitational Instability of the Solar Protoplanetary Disk

The gravitational instability of a homogeneous isotropic infinite gravitating gaseous medium is investigated in order to study the physical processes that take place during the formation of the solar planetary system. The analytical and numerical solutions of the motion equations of such a medium are considered in two approximations: cold gas and gas at a finite temperature. The real solutions describing the behavior of both wave density disturbances of a homogeneous medium and single disturbances are obtained. Waves of gravitational instability whose amplitude grows exponentially and whose highs and lows, as well as their nodal points, retain their positions in space follow the basic laws of Jean’s model. The authors interpret this wave of instability as an analogue of protoplanetary rings, which can be formed in protoplanetary disks. According to the numerical calculation results, the reaction of a homogeneous gravitating medium to the single initial perturbation of its density is significantly different from the laws of Jean’s model. The instability localized in single initial perturbations extends to the region λ < λ_J, although in this case the growth of the perturbation density is considerably less than for λ > λ_J. It is discovered that the gravitational instabilities in the region λ > λ_J suppress sound. It is shown that, without taking into account the rotation of the Sun’s protoplanetary disk medium, its critical density in the event of a large-scale gravitational instability is about four orders of magnitude smaller than the critical density in accordance with the theory of planet formation by the accumulation of solids and particles.     

Linear complexity problems of level sequences of Euler quotients and their related binary sequences欧拉商的权位序列及其二元序列的线性复杂度问题

The Euler quotient modulo an odd-prime power p^r (r > 1) can be uniquely decomposed as a p-adic number of the form \(\frac{{u^{(p - 1)p^{r - 1} } - 1}}{{p^r }} \equiv a_0 (u) + a_1 (u)p + \cdots + a_{r - 1} (u)p^{r - 1} (\bmod p^r ), \gcd (u,p) = 1,\) where 0 ? a_j (u) < p for 0 ? j ? r?1 and we set all a_j (u) = 0 if gcd(u, p) > 1. We firstly study certain arithmetic properties of the level sequences (a_j (u))_u?0 over \(\mathbb{F}_p \) via introducing a new quotient. Then we determine the exact values of linear complexity of (a_j (u))_u?0 and values of k-error linear complexity for binary sequences defined by (a_j (u))_u?0.     

Generalized Tweakable Even-Mansour Cipher and Its Applications

This paper describes a generalized tweakable blockcipher HPH (Hash-Permutation-Hash), which is based on a public random permutation P and a family of almost-XOR-universal hash functions \( \mathcal{H}={\left\{ HK\right\}}_{K\in \mathcal{K}} \) as a tweak and key schedule, and defined as y = HPH_K((t₁, t₂), x) = P(x ⊕ H_K(t₁)) ⊕ H_K(t₂), where K is a key randomly chosen from a key space \( \mathcal{K} \), (t₁, t₂) is a tweak chosen from a valid tweak space \( \mathcal{T} \), x is a plaintext, and y is a ciphertext. We prove that HPH is a secure strong tweakable pseudorandom permutation (STPRP) by using H-coefficients technique. Then we focus on the security of HPH against multi-key and related-key attacks. We prove that HPH achieves both multi-key STPRP security and related-key STPRP security. HPH can be extended to wide applications. It can be directly applied to authentication and authenticated encryption modes. We apply HPH to PMAC1 and OPP, provide an improved authentication mode HPMAC and a new authenticated encryption mode OPH, and prove that the two modes achieve single-key security, multi-key security, and related-key security.     

Negation-Limited Complexity of Parity and Inverters

In negation-limited complexity, one considers circuits with a limited number of NOT gates, being motivated by the gap in our understanding of monotone versus general circuit complexity, and hoping to better understand the power of NOT gates. We give improved lower bounds for the size (the number of AND/OR/NOT) of negation-limited circuits computing Parity and for the size of negation-limited inverters. An inverter is a circuit with inputs x ₁,…,x _n and outputs ¬ x ₁,…,¬ x _n . We show that: (a) for n=2 ^r ?1, circuits computing Parity with r?1 NOT gates have size at least 6n?log?₂(n+1)?O(1), and (b) for n=2 ^r ?1, inverters with r NOT gates have size at least 8n?log?₂(n+1)?O(1). We derive our bounds above by considering the minimum size of a circuit with at most r NOT gates that computes Parity for sorted inputs x ₁≥???≥x _n . For an arbitrary r, we completely determine the minimum size. It is 2n?r?2 for odd n and 2n?r?1 for even n for ?log?₂(n+1)??1≤r≤n/2, and it is ?3n/2??1 for r≥n/2. We also determine the minimum size of an inverter for sorted inputs with at most r NOT gates. It is 4n?3r for ?log?₂(n+1)?≤r≤n. In particular, the negation-limited inverter for sorted inputs due to Fischer, which is a core component in all the known constructions of negation-limited inverters, is shown to have the minimum possible size. Our fairly simple lower bound proofs use gate elimination arguments in a somewhat novel way.     

Tracking frequent items over distributed probabilistic data

Tracking frequent items (also called heavy hitters) is one of the most fundamental queries in real-time data due to its wide applications, such as logistics monitoring, association rule based analysis, etc. Recently, with the growing popularity of Internet of Things (IoT) and pervasive computing, a large amount of real-time data is usually collected from multiple sources in a distributed environment. Unfortunately, data collected from each source is often uncertain due to various factors: imprecise reading, data integration from multiple sources (or versions), transmission errors, etc. In addition, due to network delay and limited by the economic budget associated with large-scale data communication over a distributed network, an essential problem is to track the global frequent items from all distributed uncertain data sites with the minimum communication cost. In this paper, we focus on the problem of tracking distributed probabilistic frequent items (TDPF). Specifically, given k distributed sites S = {S ₁, … , S _k }, each of which is associated with an uncertain database \(\mathcal {D}_{i}\) of size n _i , a centralized server (or called a coordinator) H, a minimum support ratio r, and a probabilistic threshold t, we are required to find a set of items with minimum communication cost, each item X of which satisfies P r(s u p(X) ≥ r × N) > t, where s u p(X) is a random variable to describe the support of X and \(N={\sum }_{i=1}^{k}n_{i}\). In order to reduce the communication cost, we propose a local threshold-based deterministic algorithm and a sketch-based sampling approximate algorithm, respectively. The effectiveness and efficiency of the proposed algorithms are verified with extensive experiments on both real and synthetic uncertain datasets.