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Through extensive Monte Carlo simulations, we systematically study the effect of chain stiffness on the packing ability of linear polymers composed of hard spheres in extremely confined monolayers, corresponding effectively to 2D films. First, we explore the limit of random close packing as a function of the equilibrium bending angle and then quantify the local and global order by the degree of crystallinity and the nematic or tetratic orientational order parameter, respectively. A multi-scale wealth of structural behavior is observed, which is inherently absent in the case of athermal individual monomers and is surprisingly richer than its 3D counterpart under bulk conditions. As a general trend, an isotropic to nematic transition is observed at sufficiently high surface coverages, which is followed by the establishment of the tetratic state, which in turn marks the onset of the random close packing. For chains with right-angle bonds, the incompatibility of the imposed bending angle with the neighbor geometry of the triangular crystal leads to a singular intra- and inter-polymer tiling pattern made of squares and triangles with optimal local filling at high surface concentrations. The present study could serve as a first step toward the design of hard colloidal polymers with a tunable structural behavior for 2D applications. [ABSTRACT FROM AUTHOR]

Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single-molecule experimental techniques and give insight into biologically relevant processes in vivo. In this paper, we determine the transverse position and bending correlation functions for a wormlike chain confined within slits and cylinders (with one and two confined dimensions, respectively) using a mean-field approach that enforces rigid constraints on average. We show the theoretical predictions accurately capture the statistics of a wormlike chain from Monte Carlo simulations in both confining geometries for both weak and strong confinement. We also show that the longitudinal correlation function is accurately computed for a chain confined to a slit and leverages the accuracy of the model to suggest an experimental technique to infer the (often unobservable) transverse statistics from the (directly observable) longitudinal end-to-end distance. [ABSTRACT FROM AUTHOR]

Cryptographic Boolean functions play an important role in the design of symmetric ciphers. Many cryptographic criteria such as balancedness, nonlinearity, correlation immunity and transparency order are connected with the Walsh support of a Boolean function. However, we still know little about the possible structure of the Walsh supports of Boolean functions. In 2005, Carlet and Mesnager studied the Walsh supports of Boolean functions and constructed a class of n -variable Boolean functions whose Walsh support is F 2 n ∖ { 0 } , for n ≥ 10. For n ≤ 6 , it can be verified using the computer that there is no Boolean function with the Walsh Support F 2 n ∖ { 0 }. However, concerning the values of n = 7 , 8 , 9 , it has been an open problem for many years. In this paper, we construct two classes of balanced Boolean functions with the maximum possible Walsh support F 2 n ∖ { 0 } , and partially solve this problem. The first class of functions are of odd variables with n ≥ 9 , and the second class of functions are constructed based on the Maiorana–McFarland bent functions, which are of even variables with n ≥ 8. As a result, the above open problem has been settled for n = 8 , 9 , and the only unsolved case is n = 7. [ABSTRACT FROM AUTHOR]

We study the essential properties of weakly regular p-ary bent functions of ℓ -form, where a p-ary function is from F p m to F p . We observe that most of studies on a weakly regular p-ary bent function f with f (0) = 0 of ℓ -form always assume the gcd-condition: gcd (ℓ - 1 , p - 1) = 1 . We first show that whenever considering weakly regular p-ary bent functions f with f (0) = 0 of ℓ -form, we can drop the gcd-condition; using the gcd-condition, we also obtain a characterization of a weakly regular bent function of ℓ -form. Furthermore, we find an additional characterization for weakly regular bent functions of ℓ -form; we consider two cases m being even or odd. Let f be a weakly regular bent function of ℓ -form preserving the zero element; then in the case that m is odd, we show that f satisfies gcd (ℓ , p - 1) = 2 . On the other hand, when m is even and f is also non-regular, we show that f satisfies gcd (ℓ , p - 1) = 2 as well. In addition, we present two explicit families of regular bent functions of ℓ -form in terms of the gcd-condition. [ABSTRACT FROM AUTHOR]

Molecular motor amphiphiles have already been widely attempted for dynamic nanosystems across multiple length‐scale for developments of small functional materials, including controlling macroscopic foam properties, amplifying motion as artificial molecular muscles, and serving as extracellular matrix mimicking cell scaffolds. However, limiting examples of bola‐type molecular motor amphiphiles are considered for constructing macroscopic biomaterials. Herein, this work presents the designed two second generation molecular motor amphiphiles, motor bola‐amphiphiles (MBAs). Aside from the photoinduced motor rotation of MBAs achieved in both organic and aqueous media, the rate of recovering thermal helix inversion step can be controlled by the rotor part with different steric hindrances. Dynamic assembled structures of MBAs are observed under (cryo)‐transmission electron microscopy (TEM). This dynamicity assists MBAs in further assembling as macroscopic soft scaffolds by applying a shear‐flow method. Upon photoirradiation, the phototropic bending function of MBA scaffolds is observed, demonstrating the amplification of molecular motion into macroscopic phototropic bending functions at the macroscopic length‐scale. Since MBAs are confirmed with low cytotoxicity, human bone marrow‐derived mesenchymal stem cells (hBM‐MSCs) can grow on the surface of MBA scaffolds. These results clearly demonstrate the concept of designing MBAs for developing photoresponsive dynamic functional materials to create new‐generation soft robotic systems and cell‐material interfaces. [ABSTRACT FROM AUTHOR]

In the mechanics of materials, the integral method is often used to calculate the bending deformation of the beam. It is relatively simple to use this method under a single load. However, in real life, the load conditions of most beams are complex and diverse, resulting in more segmentation of the bending equation, too many integral constants, complicated equations involved, cumbersome calculation process, and heavy calculation. In order to solve this problem, the concept of singular function is introduced in this paper. By using a bending equation to express the bending moment internal force of the whole beam, and there are only two integral constants after integration, which greatly simplifies the calculation process and reduces the calculation amount. This paper mainly introduces the properties of the singular function and how to use the singular function to express the bending equation of the beam, and solves the bending deformation of the beam with the boundary conditions, and discusses the application of the singular function in the calculation of the statically indeterminate beam. [ABSTRACT FROM AUTHOR]

Let p be an odd prime. We review the characterization of p-valued Maiorana-McFarland bent functions with the Reed-Muller and the Reed-Muller-Fourier Transforms. We show that both transforms generate the same characterization and, based on the orthogonality of vectors, we prove why this is possible. Following the Language Philosopher Ludwig von Wittgenstein we consider this as a case of Family Resemblance. [ABSTRACT FROM AUTHOR]

In this article, we identify certain instances of bent functions, constructed using the so-called P τ property, that are provably outside the completed Maiorana–McFarland ( M M # ) class. This also partially answers an open problem in posed by Kan et al. (IEEE Trans Inf Theory, https://doi.org/10.1109/TIT.2022.3140180, 2022). We show that this design framework (using the P τ property), can provide instances of bent functions that are outside the known classes of bent functions, including the classes M M # , C , D and D 0 , where the latter three were introduced by Carlet in the early nineties. We provide two generic methods for identifying such instances, where most notably one of these methods uses permutations that may admit linear structures. For the first time, a set of sufficient conditions for the functions of the form h (y , z) = T r (y π (z)) + G 1 (T r 1 m (α 1 y) , ... , T r 1 m (α k y)) G 2 (T r 1 m (β k + 1 z) , ... , T r 1 m (β τ z)) + G 3 (T r 1 m (α 1 y) , ... , T r 1 m (α k y)) to be bent and outside M M # is specified without a strong assumption that the components of the permutation π do not admit linear structures. [ABSTRACT FROM AUTHOR]

ZnO nanofibers were synthesized via a hydrothermal method. A single nanofiber was delicately transferred and deposited onto a TiNx thin film on a silicon substrate to facilitate the investigation of its piezotronic properties. An aluminum-coated atomic force microscope tip was employed in contact mode as a top nanoscale electrode to locally induce bending deformation in the individual ZnO nanofiber. The current--voltage (I-V) characteristics recorded between the top atomic force microscope tip electrode and the bottom TiNx surface exhibited rectifying behavior, indicative of the formation of a Schottky junction upon the application of a minimum bending force of 25 nN by the atomic force microscope tip. This force threshold was necessary to ensure adequate contact between the atomic force microscope probe and the ZnO nanofiber. However, upon exceeding the 25 nN bending force perpendicular to the c-axis, the forward current underwent a substantial reduction, eventually leading to complete suppression of the Schottky junction under further increments in the bending force. Finite element method simulations elucidated the presence of piezoelectric activity within the ZnO nanofiber, which was responsible for the observed attenuation in the forward current. The Cheung--Cheung method was employed to quantify the increase in barrier height at the Schottky junction as a function of the applied bending force. [ABSTRACT FROM AUTHOR]

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In the present study, a new tapered finite element is developed by incorporating the in‐plane effect in our recently introduced element for the vibration analysis of internally tapered laminated plates. Stress and strain fields for a laminated plate with varying thickness along two orthogonal directions are expressed through extending classical laminated plate theory. Shape functions regarding bending and membrane behavior are extracted from the bending and axial basic displacement functions of the Euler‐Bernoulli beam, respectively. Several laminated plates with different taper configurations have been studied, and the results obtained from vibration analysis are compared with those of the literature. Since the element can capture the exact form of variation in thickness, the solution has shown to be competitively accurate with considerably fewer total degrees of freedom and elements in comparison with conventional finite elements. Highlight: A new finite element for thin, tapered, laminated plates is introduced.Laminates' stiffness matrix is obtained for arbitrary thickness variation.A novel method is adopted to derive in‐plane shape functions.C1 continuity is guaranteed along the edges of elements.Calculation cost is considerably reduced. [ABSTRACT FROM AUTHOR]

We obtain geometric characterizations of the dual functions for quadratic bent and vectorial bent functions in terms of quadrics. Additionally, using the zeros of the polynomial X q + 1 + X + a which have been studied recently in the literature, we provide some examples of binomial quadratic bent functions on F q 4 and F q 6 , where q is a power of 2. [ABSTRACT FROM AUTHOR]

Natural vibration characteristics of a cantilever beam that is parametrically excited by pitch motion are theoretically investigated in this work. A partial differential equation governing the parametrically excited bending vibration of the beam is established by employing the generalized Hamiltonian principle. Normal modal functions of the bending vibration are obtained based on the method of separation of variables. It reveals that the dynamic pitch motion cannot change the modal shapes of the bending vibration of a uniform beam. Principal vibrations of the beam are studied by taking into account two cases of E I 1 = E I 2 and E I 1 ≠ E I 2 , where E I 1 and E I 2 are the first and second principal bending stiffness, respectively. The bending stiffness is considered as the superposition of a constant stiffness with a small perturbation. With the aid of the Fourier series theory and the method of multiple scales, the principal vibrations of the parametrically excited system at non-resonant and resonant cases are analyzed by introducing a small natural parameter , while natural vibration characteristics of the beam are obtained and the orthogonal properties of modal functions are illustrated. Theoretical methods provided in this work are verified by using the finite element method, assumed modes method and direct numerical integrations to the governing equation based on a rectangular beam model. It reveals that theoretical results coincide with numerical results very well. Finally, the influences of design parameters including the beam height, beam width, beam length, slender ratio, aspect ratio, pitch amplitude, pitch frequency and pitch phase on natural frequencies of a harmonic pitching beam are discussed. It shows that the width, height, length, slender ratio, aspect ratio and pitch amplitude have dramatic influences on the natural frequencies of the pitching beam, while the pitch frequency and pitch phase have little effect on natural frequencies. [ABSTRACT FROM AUTHOR]

The construction of (minimal) linear codes from functions has received much attention in the literature. In this paper, we derive several minimal codes from the sets of pre-images of weakly regular plateaued and bent functions over the odd characteristic finite fields. Based on the recent construction method, we obtain six-weight and seven-weight minimal codes from these functions. The Hamming weights in proposed codes are calculated from the character sums of the sets based on the Walsh spectrum of the employed functions, while the weight distributions of the codes are determined from both the sizes of the employed sets and the Walsh distributions of the employed functions. [ABSTRACT FROM AUTHOR]

Boolean functions used in symmetric-key encryption should have high higher-order nonlinearity to resist several known cryptographic attacks, such as algebraic attacks and low-degree approximation attacks. The higher-order nonlinearity also plays an important role in coding theory and theoretical computer science, since it relates to the covering radius of Reed–Muller codes and the Gowers norm, respectively. It is well-known that bent functions have the highest nonlinearity in an even number of variables and thus they possess the best ability to withstand fast correlation attacks and best affine approximation attacks. However, there is currently limited knowledge regarding the higher-order nonlinearity of bent functions because computing the higher-order nonlinearity, or even providing tight lower bounds, is an extremely hard task. In 1974, Dillon proposed two well-known classes of bent functions based on partial spread (in brief, PS), called PS − and PS + , respectively. He also exhibited a subclass of bent functions in PS − , known as partial spread affine plane(PS a p for short). In this paper, we provide a lower bound on the third-order nonlinearity of the simplest PS a p bent functions in n variables, where n ≥ 6 is even, by calculating the nonlinearities of all second-order derivatives of this kind of bent functions. Compared to the two known lower bounds on the third-order nonlinearity given by Carlet and Tang et al. respectively, our lower bound is much better than these two ones. [ABSTRACT FROM AUTHOR]

Rotor-Active magnetic bearing (rotor-AMB) systems offer significant advantages in power consumption and are increasingly being applied in fluid machinery. However, in such machinery, the impeller and the rotor are commonly connected by bolt fastening. Once a certain pre-tightening force is applied to the bolted connection and the interface contact between the rotor and the impeller is formed, the flexible modal vibration will be excited when the rotor is levitated. The conventional Proportional-Integral-Derivative (PID) controller is limited in this vibration suppression and it is essential to increase the damping at bending mode to inhibit vibration. However, the calculation of the optimal phase compensated is based on the rotor-AMB model considering interface contact. In this work, the effect of the interface contact is equivalent to massless spring units, and the disturbance generated by spring units is acted upon the mechatronic system in the way of positive feedback. The detailed description of the transfer function from the disturbance to rotor deformation at fourth bending mode is obtained by theoretical model and system identification. The optimal phase of the system needed to inhibit the disturbance is determined by minimizing the gain of the transfer function at fourth bending mode. A combination of PID control and phase compensation is implemented in the experiment. The results show that the optimal phase is 50° as the calculation and the optimal phase compensation control can sufficiently inhibit the modal vibration. [ABSTRACT FROM AUTHOR]

In this paper we give three constructions of cyclic self-orthogonal codes over Z 2 k , for k ≥ 3 , from Boolean functions on n variables. The first construction for each k, 3 ≤ k ≤ n , yields a self-orthogonal Z 2 k -code of length 2 n + 2 with all Euclidean weights divisible by 2 k + 1. In the remaining two constructions, for each even n and k ≥ 3 , we generate a self-orthogonal Z 2 k -code of length 2 n + 1. All Euclidean weights in the constructed code are divisible by 2 2 k - 1 or 2 k + 1 , depending on which of the two constructions is used. [ABSTRACT FROM AUTHOR]

Numerical modeling of kinematical and dynamical X‐ray diffraction in a bent crystal was performed on the basis of two approaches to integrating the Takagi–Taupin equations, and using two‐dimensional recurrence relations. Within the framework of kinematical diffraction, a new equation is obtained that describes the distribution of diffracted intensity inside a bent crystal. The time taken for numerical calculations based on this equation is significantly reduced in comparison with the use of algorithms of the dynamical diffraction theory. The simulation shows for the first time that, for strongly bent crystals, the maximum value of the diffraction intensity is formed inside the deformed structure and not on its surface. In the case of strong bending of the crystal structure, the deviation of the X‐ray beam from the Bragg angle does not change the diffraction pattern but shifts it along the lateral direction. The results of calculations of diffraction in a strongly bent crystal based on the equations of dynamical and kinematical diffraction coincide, while the computations for weakly bent crystals differ. The possibility of estimating the primary extinction length of a bent crystal as a function of the bending radius is shown. In the case of kinematical diffraction in bent crystalline microsystems, a new method has been developed to calculate X‐ray reciprocal‐space mapping. [ABSTRACT FROM AUTHOR]

In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions in the most general setting, generalizing several results that were achieved under specific constraints. For the particularly interesting elementary abelian case, we derive several new strong conditions and classification results on the value distributions. Moreover, we show that most of the classical constructions of perfect nonlinear functions have very specific value distributions, in the sense that they are almost balanced. Consequently, we completely determine the possible value distributions of vectorial Boolean bent functions with output dimension at most 4. Finally, using the discrete Fourier transform, we show that in some cases value distributions can be used to determine whether a given function is perfect nonlinear, or to decide whether given perfect nonlinear functions are equivalent. [ABSTRACT FROM AUTHOR]

We consider Niho bent functions in small dimensions. They are in one-to-one correspondence with ovals in the projective plane PG(2, q), q = 2m. Niho bent functions and ovals are listed up to equivalency for dimensions m ≤ 6. They are described by means of g-functions. We also give characterization of supports of Niho bent functions and their duals in terms of associated ovals. [ABSTRACT FROM AUTHOR]

Aaronson defined Forrelation (2010) as a measure of correlation between a Boolean function f and the Walsh–Hadamard transform of another function g . In a recent work, we have studied different cryptographically important spectra of Boolean functions through the lens of Forrelation. In this paper, we explore a similar kind of correlation in terms of nega-Hadamard transform. We call it nega-Forrelation and obtain a more efficient sampling strategy for nega-Hadamard transform compared to the existing results. Moreover, we present an efficient sampling strategy for nega-crosscorrelation (and consequently nega-autocorrelation) spectra too, by tweaking the nega-Forrelation technique. Finally, we connect the hidden shift finding algorithm for bent functions (Rötteler, 2010) with the Forrelation algorithm and extend it for the negabent functions. [ABSTRACT FROM AUTHOR]

A Boolean function f on n variables is said to be a bent function if the absolute value of all its Walsh coefficients is 2 n / 2 . Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on a modification of the Maiorana–McFarland family of bent functions and recent progress in the estimation of the number of transversals in latin squares and hypercubes. By-products of our proofs are the asymptotics of the logarithm of the numbers of partitions of the Boolean hypercube into 2-dimensional affine and linear subspaces. [ABSTRACT FROM AUTHOR]

Recently, several interesting constructions of vectorial Boolean functions with the maximum number of bent components (MNBC functions, for short) were proposed. However, many of them have component functions from the completed Maiorana-McFarland class M # . Moreover, no examples of MNBC functions containing component functions provably outside M # are known. In this paper, we classify all MNBC functions in six variables. Based on the analysis of the obtained equivalence classes, we propose several infinite families of MNBC functions with component functions outside the M # class. In particular, two of our new constructions are solutions to the open problem [Bapić et al (eds) Proceedings of the twelfth international workshop on coding and cryptography, 2022, Item 1., p. 9]. [ABSTRACT FROM AUTHOR]

The substitution box (S-box) is the core component of any block cipher that creates confusion in the ciphertext. This research contributes to creating a substitution box based on bent Boolean functions. Bent Boolean functions are constructed using the Maiorana–McFarland method and used as the coordinate functions of the substitution box. They are maximal nonlinear and inherently imbalanced, making them unsuitable for direct use in constructing a confusion component. The imbalance nature of the coordinate Boolean function directly impacts the bijective property of the nonlinear component. To create a bijective confusion component, we focus on mitigating the imbalance of each coordinate Boolean function. The methodology adopted is simple and efficient as compared to other heuristic techniques. By defining an empty matrix and putting bent Boolean functions side by side as matrix elements, we shape the initial 2 n × k sized substitution box, k ∈ (2 ,... , n) . We limit the number of occurrences of each possible outcome of initial 2 n × k substitution box to make a bijective n × n S-box. These small initial S-boxes lay a good foundation for constructing strong subsequent S-boxes. Experimental results based on the generation of 8 × 8 substitution box indicate that the suggested algorithm outperforms other competing heuristic approaches in nonlinearity, while maintaining sufficient performance in the strict avalanche criterion, bit-independence, linear and differential probability properties. The suggested nonlinear component is tested using well-known images from the literature, and the histogram analysis of the confused images demonstrates a high degree of randomness. [ABSTRACT FROM AUTHOR]

The large‐pore interconnected channels in cryogels, allow convectional flow and rapid mass‐transport of solute constituents between the solution and cryogel polymer framework, as compared to slower, diffusionally‐controlled mass‐transport in small‐pore hydrogels. These features are applied to develop enzyme‐loaded polyacrylamide (pAAm) cryogels, and glucose oxidase (GOx)‐loaded pH‐responsive DNA‐based pAAm cryogels, revealing enhanced biocatalytic transformations, enhanced temporal stiffness changes, and mechanical bending functions, as compared to analog hydrogels. DNA‐based pAAm cryogel/hydrogel matrices, revealing pH‐switchable stiffness properties through reversible reconfiguration of DNA‐bridging units into i‐motif structures, are introduced. Enhanced switchable stiffness changes of DNA‐based pAAm cryogels, as compared to analog hydrogels, are demonstrated upon subjecting the cryogel/hydrogel matrices to auxiliary pH‐changes, or by integration of GOx into the frameworks, and driving pH‐changes through GOx‐catalyzed aerobic oxidation of glucose to gluconic acid. Enhanced stiffness changes of pAAm cryogels represent a major advance to control the mechanical properties of cryogels and are attributed to the convectionally‐controlled mass‐transport in the cryogel matrices. Moreover, bilayer constructs consisting of poly‐N‐isopropylacrylamide (pNIPAM) cryogels and pH‐responsive DNA‐based pAAm cryogel or hydrogel structures are constructed. Enhanced pH/glucose triggered mechanical bending rates of the pNIPAM cryogel/pAAm cryogel or pNIPAM cryogel/GOx‐loaded pAAm cryogel, as compared to analog pNIPAM cryogel/pAAm hydrogel frameworks are demonstrated. [ABSTRACT FROM AUTHOR]

The current study investigated the geometry optimization of a hybrid-driven (based on the combination of air pressure and tendon tension) soft robot for use in robot-assisted intra-bronchial intervention. Soft robots, made from compliant materials, have gained popularity for use in surgical interventions due to their dexterity and safety. The current study aimed to design a catheter-like soft robot with an improved performance by minimizing radial expansion during inflation and increasing the force exerted on targeted tissues through geometry optimization. To do so, a finite element analysis (FEA) was employed to optimize the soft robot's geometry, considering a multi-objective goal function that incorporated factors such as chamber pressures, tendon tensions, and the cross-sectional area. To accomplish this, a cylindrical soft robot with three air chambers, three tendons, and a central working channel was considered. Then, the dimensions of the soft robot, including the length of the air chambers, the diameter of the air chambers, and the offsets of the air chambers and tendon routes, were optimized to minimize the goal function in an in-plane bending scenario. To accurately simulate the behavior of the soft robot, Ecoflex 00-50 samples were tested based on ISO 7743, and a hyperplastic model was fitted on the compression test data. The FEA simulations were performed using the response surface optimization (RSO) module in ANSYS software, which iteratively explored the design space based on defined objectives and constraints. Using RSO, 45 points of experiments were generated based on the geometrical and loading constraints. During the simulations, tendon force was applied to the tip of the soft robot, while simultaneously, air pressure was applied inside the chamber. Following the optimization of the geometry, a prototype of the soft robot with the optimized values was fabricated and tested in a phantom model, mimicking simulated surgical conditions. The decreased actuation effort and radial expansion of the soft robot resulting from the optimization process have the potential to increase the performance of the manipulator. This advancement led to improved control over the soft robot while additionally minimizing unnecessary cross-sectional expansion. The study demonstrates the effectiveness of the optimization methodology for refining the soft robot's design and highlights its potential for enhancing surgical interventions. [ABSTRACT FROM AUTHOR]

Bent functions are Boolean functions in even number of variables that have maximal nonlinearity. They have flat Walsh–Hadamard spectrum and are of interest for their applications in algebra, coding theory and cryptography. A bent function is called self-dual if it coincides with its dual bent function. In current work we study the decomposition of the form f 0 , f 1 , ... , f 2 k - 1 of the vector of values of a self-dual bent function, formed by the concatenation of 2 k Boolean functions f j in n - k variables. We treat the cases k = 1 , 2 . Based on a spectral characterization, we introduce a notion of self-dual near-bent function in odd number of variables and prove that there exists a one-to-one correspondence between the notions of self-duality for even and odd number of variables. As a result the characterization for the decomposition f 0 , f 1 is obtained. For the decomposition f = f 0 , f 1 , f 2 , f 3 we prove that if sign vectors of subfunctions f j are linearly dependent, then all these subfunctions are bent. We prove that for n ⩾ 6 the converse does not hold, that is the obtained condition is sufficient only. These results are also generalized for the case of an arbitrary bent function. Three new iterative constructions of self-dual bent functions are proposed. One of them allows to build a class of self-dual bent functions which cannot be decomposed into the concatenation of four bent functions. Based on the constructions a new iterative lower bound on the cardinality of the set of self-dual bent functions is obtained. [ABSTRACT FROM AUTHOR]

p-valued Maiorana-McFarland bent functions exist, as in the binary case, only for an even number of variables and they are normally associated to their Discrete Fourier spectra in order to specify their bentness through the flatness of the spectra. In this paper, a closely related, but different approach is considered. Structural properties of the Reed-Muller spectra of p-valued MaioranaMcFarland bent functions are studied when p > 2 is a prime. It is shown that the Reed-Muller spectra of p-valued Maiorana-McFarland bent functions have a regressive structure, parameterized by p and k, where n = 2k denotes the even number of variables. [ABSTRACT FROM AUTHOR]

Self-orthogonal codes are linear codes such that they are contained in their duals. Self-orthogonal codes have attracted much attention due to their applications in linear complementary dual codes (LCD codes for short), quantum codes, row-self-orthogonal matrices and so on. In this paper, we first construct several families of ternary self-orthogonal codes from weakly regular bent functions. The parameters and weight distributions of them are determined. Then we use the self-orthogonal codes to construct new infinite families of ternary LCD codes. Some LCD codes are optimal according to the Code Tables at http://www.codetables.de/. [ABSTRACT FROM AUTHOR]

Macromolecular crowding is a feature of cellular and cell-free systems that, through depletion effects, can impact the interactions of semiflexible biopolymers with surfaces. In this work, we use computer simulations to study crowding-induced adsorption of semiflexible polymers on otherwise repulsive surfaces. Crowding particles are modeled explicitly, and we investigate the interplay between the bending stiffness of the polymer and the volume fraction and size of crowding particles. Adsorption to flat surfaces is promoted by stiffer polymers, smaller crowding particles, and larger volume fractions of crowders. We characterize transitions from non-adsorbed to partially and strongly adsorbed states as a function of bending stiffness. The crowding-induced transitions occur at smaller values of the bending stiffness as the volume fraction of crowders increases. Concomitant effects on the size and shape of the polymer are reflected by crowding- and stiffness-dependent changes to the radius of gyration. For various polymer lengths, we identify a critical crowding fraction for adsorption and analyze its scaling behavior in terms of polymer stiffness. We also consider crowding-induced adsorption in spherical confinement and identify a regime in which increasing the bending stiffness induces desorption. The results of our simulations shed light on the interplay of crowding and bending stiffness on the spatial organization of biopolymers in encapsulated cellular and cell-free systems. [ABSTRACT FROM AUTHOR]

In this paper, we first study exponential sums of the form ∑ x ∈ F q ψ (f (x)) χ (g (x)) called hybrid character sums, where f , g are functions over finite field F q , ψ is a nontrivial multiplicative character and χ is a nontrivial additive character of F q. The absolute values or explicit values of them are determined under certain conditions. We then present several constructions of complex codebooks which are also called frames. The proposed codebooks are constructed from Hadamard matrices with binary row selection sequences. The hybrid character sums play an important role in determining the maximum magnitude of the inner products between vectors in these codebooks. It is proved that the magnitude of the inner products between distinct code vectors of each codebook is two-valued, and the maximum magnitude of each codebook asymptotically achieves the Welch bound equality. The constructed codebooks are equivalent to nearly equiangular tight frames and have nice application in compressed sensing matrices. [ABSTRACT FROM AUTHOR]

Nucleic acids are highly deformable helical molecules constantly stretched, twisted and bent in their biological functioning. Single molecule experiments have shown that double stranded (ds)-RNA and standard ds-DNA have opposite twist-stretch patterns and stretching properties when overwound under a constant applied load. The key structural features of the A-form RNA and B-form DNA helices are here incorporated in a three-dimensional mesoscopic Hamiltonian model which accounts for the radial, bending and twisting fluctuations of the base pairs. Using path integral techniques which sum over the ensemble of the base pair fluctuations, I compute the average helical repeat of the molecules as a function of the load. The obtained twist-stretch relations and stretching properties, for short A- and B-helical fragments, are consistent with the opposite behaviors observed in kilo-base long molecules. [ABSTRACT FROM AUTHOR]

The current study examined the linear and nonlinear bending results of functionally graded graphene nanoplatelet reinforced composite beams. The equation system was constructed using Reddy's third order shear deformation theory and a von Kármán type nonlinear strain-displacement relationship. The nonlinear bending results of this system were solved using the Gram-Schmidt-Ritz method in conjunction with the direct iteration technique. By employing the Gram-Schmidt orthogonalization procedure for generating shape functions in the method, numerically stable functions for nonlinear bending analysis of beams were obtained. Our solutions were validated for accuracy by comparing them to some published results. The numerical results indicate that the geometrical nonlinearity of beams subjected to uniform distributed load is greater than that of beams subjected to sinusoidal, linear, or parabolic distributed loads. New results on several significant effects of reinforcement patterns, graphene nanoplatelet weight fraction, and different types of distributed loads are presented and discussed in this study, in which the findings can serve as a benchmark for future research. [ABSTRACT FROM AUTHOR]

Boolean functions form the fundamental components of symmetric cryptographic systems, serving as the building blocks. Modifying bent functions makes it feasible to design Boolean functions with desired properties that exhibit high non-linearity. The current study offers a comprehensive analysis of bent functions through its support, culminating in the introduction of an algorithm for the systematic construction of four variable bent functions. This algorithm enables the complete generation of all 896 fourvariable bent functions. Furthermore, we introduce a methodology for constructing n-variable bent functions (where n > 4), leveraging both the algorithm and an established secondary technique for bent function construction. Lastly, we examine the estimation of the count of bent functions by utilising certain properties associated with the support of bent functions. [ABSTRACT FROM AUTHOR]

The rapid development of new classes of automotive steels such as the 3rd generation of advanced high-strength steels has created the need for the efficient characterization of their mechanical properties in loading scenarios other than uniaxial tension. The VDA 238-100 tight radius bend test has gained widespread acceptance in recent years for characterizing performance in plane strain bending, but there is uncertainty surrounding the use of the bend angle and its interrelation with the test parameters. The objective of the present study is to investigate the intertwined effects of the sheet thickness, bend radius, and tensile properties upon the bendability of seven advanced high-strength steels in different thicknesses for a total of 83 conditions. Practical correlations are developed to predict the bend angle and plane strain fracture strain as functions of the bending conditions and tensile mechanical properties. An extensive dataset comprising 26 additional advanced high-strength steel test cases was compiled from the literature to evaluate the proposed correlation for the plane strain fracture strain. [ABSTRACT FROM AUTHOR]

All‐liquid molding can be used to transform a liquid into free‐form solid constructs, while maintaining internal fluidity. Traditional biological scaffolds, such as cured pre‐gels, are normally processed in solid state, sacrificing flowability and permeability. However, it is essential to maintain the fluidity of the scaffold to truly mimic the complexity and heterogeneity of natural human tissues. Here, this work molds an aqueous biomaterial ink into liquid building blocks with rigid shapes while preserving internal fluidity. The molded ink blocks for bone‐like vertebrae and cartilaginous‐intervertebral‐disc shapes, are magnetically manipulated to assemble into hierarchical structures as a scaffold for subsequent spinal column tissue growth. It is also possible to join separate ink blocks by interfacial coalescence, different from bridging solid blocks by interfacial fixation. Generally, aqueous biomaterial inks are molded into shapes with high fidelity by the interfacial jamming of alginate surfactants. The molded liquid blocks can be reconfigured using induced magnetic dipoles, that dictated the magnetic assembly behavior of liquid blocks. The implanted spinal column tissue exhibits a biocompatibility based on in vitro seeding and in vivo cultivating results, showing potential physiological function such as bending of the spinal column. [ABSTRACT FROM AUTHOR]

Using polar coordinates, we consider descriptions of translation, Subiaco and Adelaide hyperovals in terms of exponential sums and Kloosterman sums. As an application, we describe a new construction of hyperbent functions that belong to the Charpin and Gong's family. Explicit examples of this construction are provided as functions with multiple trace terms via Dillon-like exponents. [ABSTRACT FROM AUTHOR]

In this paper, we study further three kinds of bent functions (binary, p-ary and gbent) related to spreads. We characterize those p-ary bent functions whose restrictions to the elements of the Dillon spread are affine. A technique for using finite pre-quasifield spreads (from finite geometry) to construct p-ary bent functions and generalized bent functions is studied and applied. [ABSTRACT FROM AUTHOR]

We perform numerical simulations of active semiflexible filaments inside a rigid spherical cavity. We study the problem as a function of the bending rigidity, degree of confinement, and strength of the active forces. For passive filaments, the multispool conformations already established in previous studies are recovered, yet even small amounts of activity, when aligned along the direction of the filament backbone, destabilize these passive conformations. What emerges from our study is a highly dynamic scenario, where a filament is capable of escaping local and global energy minima and sample, in a quasiperiodic fashion, an ensemble of conformations usually associated with higher bending energies, and previously observed for passive filaments only under very different degrees of confinement or identified as glassy metastable states. We detail the structural properties of the different states and uncover a new dynamic pathway associated with their formation. [ABSTRACT FROM AUTHOR]

This document is an editorial note for a special issue on Multiple Valued Logic in the Journal of Applied Logics. The note highlights the importance of Multiple Valued Logic in the context of the imminent change in technology towards quantum computing. The special issue includes papers in three different areas: circuits, computing and algorithms, and theory. The papers cover topics such as data transmission quality evaluation, quantum algorithms for covering problems, embedding first-order logic into higher order intuitionistic logic, weak bases for computational problems, representation of maximally asymmetric functions, and p-valued Maiorana-McFarland functions. The note concludes by expressing the belief that this special issue will contribute to the study of the latest trends in Multiple Valued Logic. [Extracted from the article]

In the sheet forming process, the final bending angle is mostly determined based on experience rather than based on a reliable theoretical framework. Furthermore, the local bent areas tend to decrease in thickness. Thus, it is difficult to control the quality of the final products. In this study, we developed an optimized bending angle function by combining segment boundaries to improve the final sheet forming quality and reduce the local thinning defects. The finite element submodel method was used to establish a high-definition thickness-sensitive numerical model for the bottom bending area of the hat-shaped part. This method accurately simulated the thickness variation law of the bending area of roll forming and analyzed the optimization function of the bending angle of the segment boundary as well as the process parameters for local thinning. Finally, roll-bending experiments were conducted to analyze the bending angle distribution conditions and the change law with respect to the process parameters of the cap-shaped parts in case of local thinning defects to verify the accuracy of the finite element simulation process. The results showed that the local thinning defect in the bending area of the hat-shaped part was smaller during roll bending, and the forming quality obtained was better than that obtained using other previously reported methods. The experimental data were consistent with the simulation data, verifying the accuracy of our proposed approach. Moreover, the thickness of the thinning defect was influenced by the process parameters; the plate bending radius and yield strength increased, and thickness thinning gradually decreased. Furthermore, the local thinning defects increased with the increasing plate thickness. [ABSTRACT FROM AUTHOR]

The nonlinearity and additive nonlinearity of a function are defined as the Hamming distances, respectively, to the set of all affine mappings and to the set of all mappings having nontrivial additive translators. On the basis of the revealed relation between the nonlinearities and the Fourier coefficients of the characters of a function, convenient formulas for nonlinearity evaluation for practically important classes of functions over an arbitrary finite field are found. In the case of a field of even characteristic, similar results were obtained for the additive nonlinearity in terms of the autocorrelation coefficients. The formulas obtained made it possible to present specific classes of functions with maximal possible and high nonlinearity and additive nonlinearity. [ABSTRACT FROM AUTHOR]

Recently, balanced Boolean functions with an even number n of variables achieving very good autocorrelation properties have been obtained for 12 ≤ n ≤ 26 . These functions attain the maximum absolute value in the autocorrelation spectra (without considering the zero point) less than 2 n 2 and are found by using a heuristic search algorithm that is based on the design method of an infinite class of such functions for a higher number of variables. Here, we consider balanced Boolean functions that are closest to the bent functions in terms of the Hamming distance and perform a genetic algorithm efficiently aiming to optimize their cryptographic properties, which provides better absolute indicator values for all of those values of n for the first time. We also observe that among our results, the functions for 16 ≤ n ≤ 26 have nonlinearity greater than 2 n − 1 − 2 n 2 . In the process, our search strategy produces balanced Boolean functions with the best-known nonlinearity for 8 ≤ n ≤ 16 . [ABSTRACT FROM AUTHOR]

The influence of a variable is an important concept in the analysis of Boolean functions. The more general notion of influence of a set of variables on a Boolean function has four separate definitions in the literature. In the present work, we introduce a new definition of influence of a set of variables which is based on the auto-correlation function and develop its basic theory. Among the new results that we obtain are generalizations of the Poincar\'e inequality and the edge expansion property of the influence of a single variable. Further, we obtain new characterizations of resilient and bent functions using the notion of influence. We show that the previous definition of influence due to Fischer et al. [Proceedings of the 43rd Symposium on Foundations of Computer Science (FOCS 2002), Vancouver, BC, Canada, IEEE Computer Society, 2002, pp. 103--112] and Blais [Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, M. Mitzenmacher, ed., Bethesda, MD, ACM, 2009, pp. 151--158] is half the value of the auto-correlation based influence that we introduce. Regarding the other prior notions of influence, we make a detailed study of these and show that each of these definitions does not satisfy one or more desirable properties that a notion of influence may be expected to satisfy. [ABSTRACT FROM AUTHOR]

Since the global stability criteria for Λ-fractional mechanics have been established, the Λ-fractional beam bending problem is discussed within that context. The co-existence of the phase phenomenon is revealed, allowing for elastic curves with non-smooth curvatures. The variational bending problem in the Λ-fractional space is considered. Global minimization of the total energy function of beam bending is necessarily applied. The variational Euler-Lagrange equation yields an equilibrium equation of the elastic curve, with the simultaneous possible corners being expressed by Weierstrass-Erdmann corner conditions. [ABSTRACT FROM AUTHOR]

Soft-robotics for biomedical applications, such as rehabilitation robots, is a field of intense research activity. Different actuation solutions have been proposed in the last decades, involving study and development of soft actuators of different types and materials. The purpose of the paper is to present procedures for an optimized design, and for easy and low cost production and characterization of monolithic PneuNets soft-actuators. An innovative design approach has been developed. The parameterization of the geometry, combined with FEM simulations is the basis for an optimized design of the actuator, as a function of the obtained bending and of the generated forces. Simple and cheap characterization setup and procedures have been identified for the actuator characterization and for simulation results validation. An easy and low-cost fabrication method based on lost wax core obtained through a silicone based mold has been developed for a monolithic PneuNets soft-actuator. The proposed solution performs well in bending, without the need for a strain limiting layer. Experimental results validated simulations, confirming the feasibility of adopting an optimized simulation-based design approach. [ABSTRACT FROM AUTHOR]

During the last five decades, many different secondary constructions of bent functions were proposed in the literature. Nevertheless, apart from a few works, the question about the class inclusion of bent functions generated using these methods is rarely addressed. Especially, if such a "new" family belongs to the completed Maiorana–McFarland ( M M # ) class then there is no proper contribution to the theory of bent functions. In this article, we provide some fundamental results related to the inclusion in M M # and eventually we obtain many infinite families of bent functions that are provably outside M M # . The fact that a bent function f is in/outside M M # if and only if its dual is in/outside M M # is employed in the so-called 4-decomposition of a bent function on F 2 n , which was originally considered by Canteaut and Charpin (IEEE Trans Inf Theory 49(8):2004–2019, 2003) in terms of the second-order derivatives and later reformulated in (Hodžić et al. in IEEE Trans Inf Theory 65(11):7554–7565, 2019) in terms of the duals of its restrictions to the cosets of an (n - 2) -dimensional subspace V. For each of the three possible cases of this 4-decomposition of a bent function (all four restrictions being bent, semi-bent, or 5-valued spectra functions), we provide generic methods for designing bent functions provably outside M M # . For instance, for the elementary case of defining a bent function h (x , y 1 , y 2) = f (x) ⊕ y 1 y 2 on F 2 n + 2 using a bent function f on F 2 n , we show that h is outside M M # if and only if f is outside M M # . This approach is then generalized to the case when two bent functions are used. More precisely, the concatenation f 1 | | f 1 | | f 2 | | (1 ⊕ f 2) also gives bent functions outside M M # if f 1 or f 2 is outside M M # . The cases when the four restrictions of a bent function are semi-bent or 5-valued spectra functions are also considered and several design methods of constructing infinite families of bent functions outside M M # are provided. [ABSTRACT FROM AUTHOR]