Quickhull is an algorithm for computing the convex hull of points in a plane that performs well in practice, but has poor complexity on adversarial input. In this paper we show the same holds for the numerical stability of Quickhull.
Abstract The current research paper presents a design of a mutually coupled cascode Common Gate Common Source (CG-CS) Low Noise Amplifier (LNA) using current reuse technique. The proposed design provides a significant improvement in the gain and noise performance of the LNA, while also reducing power consumption. Mutually coupled inductors help in reducing the size of the circuit while transformer connected at the output provide output impedance matching. Proposed LNA simulated for the 4–14 GHz RF frequency. Mathematical analysis of proposed LNA has been analyzed using the small signal model henceforth input impedance; gain and Noise Figure (NF) have been derived from it. The design and simulation results show that the proposed LNA design with current reuse technique achieved a maximum gain of 17.87 dB, minimum NF of 5.45 dB, and input reflection coefficient less than –10 dB for the 10 GHz bandwidth. These results indicate a significant improvement in the overall performance of the LNA compared to conventional designs as Figure of Merit (FoM) is 17.34.
This note gives a lower bound of $Ω(n^{\lceil 2d/3\rceil})$ on the maximal complexity of the Euclidean Voronoi diagram of $n$ non-intersecting lines in $\mathbb{R}^d$ for $d>2$.
We present a row reduction algorithm to compute the barcode decomposition of persistence modules. This algorithm dualises the standard persistence one and clarifies the symmetry between clear and compress optimisations.
The construction of an unbounded polyhedron from a "jagged'' convex cap is described, and several of its properties discussed, including its relation to Alexandrov's "limit angle."
Mohsen Javadi, Hossein Miar‐Naimi, Seyed Mehdi Hosseini Andargoli
SummaryA modified common source‐common gate (CS‐CG) low‐noise transconductance amplifier (LNTA) with an improved noise figure (NF), operational bandwidth, and power consumption are analyzed in this paper. The common source (CS) stage of the modified LNTA is utilized for noise cancellation and transconductance enhancement of the common gate (CG) transistor. Using these, NF, bandwidth, and power consumption are improved without using extra active elements. Noise analyses show the modified CS‐CG LNTA has lower NF than conventional CS‐CG LNTA. The linearity of the modified CS‐CG LNTA is calculated by Taylor series expression. Besides, a design procedure is proposed based on the obtained equations for linearity and NF. Finally, an ultra‐wideband (UWB) surface acoustic wave (SAW‐less) direct‐conversion receiver is designed in 65 nm complementary metal‐oxide‐semiconductor (CMOS) technology. NF and third‐order intercept point (IIP3) of the designed receiver are simulated as 5 dB and −2 dBm, respectively. The receiver consumes 18.4 mA from a 1.8 V supply voltage.
David Bremner, Olivier Devillers, Marc Glisse
et al.
We study the following problem: Given $k$ paths that share the same vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction? We prove that for any dimension $d\geq 2$, there is a set of $d + 1$ paths that does not admit a monotone simultaneous geometric embedding.
We derive properties and a characterization of discrete composition matrices which are useful in the field of numerical computation of shape correspondences.
We show that the size-sensitive packing lemma follows from a simple modification of the standard proof, due to Haussler and simplified by Chazelle, of the packing lemma.
Background: Bladder dysfunction is a common feature of multiple sclerosis (MS). Objective: In this study we aimed to assess the efficacy, tolerability and safety of Sativex® (nabiximols) as an add-on therapy in alleviating bladder symptoms in patients with MS. Methods: We undertook a 10-week, double-blind, randomized, placebo-controlled, parallel-group trial in 135 randomized subjects with MS and overactive bladder (OAB). Results: The primary endpoint was the reduction in daily number of urinary incontinence episodes from baseline to end of treatment (8 weeks). Other endpoints included incidence of nocturia and urgency, overall bladder condition (OBC), daytime frequency, Incontinence Quality of Life (I-QOL), Patient’s Global Impression of Change (PGIC) and volume voided. The primary endpoint showed little difference between Sativex and placebo. Four out of seven secondary endpoints were significantly in favour of Sativex: number of episodes of nocturia (adjusted mean difference -0.28, p = 0.010), OBC (-1.16, p = 0.001), number of voids/day (-0.85, p = 0.001) and PGIC ( p = 0.005). Of the other endpoints, number of daytime voids was statistically significantly in favour of Sativex (-0.57, p = 0.044). The improvement in I-QOL was in favour of Sativex but did not reach statistical significance. Conclusions: Although the primary endpoint did not reach statistical significance, we conclude that Sativex did have some impact on the symptoms of overactive bladder in patients with MS, providing evidence of some improvement in symptoms associated with bladder dysfunction in these subjects.
A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.
We tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra.
In this paper, we prove the problem of stabbing a set of disjoint bends by a convex stabber to be NP-hard. We also consider the optimization version of the convex stabber problem and prove this problem to be APX-hard for sets of line segments.
Olivier Bodini, Antoine Genitrini, Frédéric Peschanski
In this paper, we study the shuffle operator on concurrent processes (represented as trees) using analytic combinatorics tools. As a first result, we show that the mean width of shuffle trees is exponentially smaller than the worst case upper-bound. We also study the expected size (in total number of nodes) of shuffle trees. We notice, rather unexpectedly, that only a small ratio of all nodes do not belong to the last two levels. We also provide a precise characterization of what ``exponential growth'' means in the case of the shuffle on trees. Two practical outcomes of our quantitative study are presented: (1) a linear-time algorithm to compute the probability of a concurrent run prefix, and (2) an efficient algorithm for uniform random generation of concurrent runs.
We use death processes and embeddings into continuous time in order to analyze several urn models with a diminishing content. In particular we discuss generalizations of the pill's problem, originally introduced by Knuth and McCarthy, and generalizations of the well known sampling without replacement urn models, and OK Corral urn models.
Let $k≥2$ be a fixed integer. Given a bounded sequence of real numbers $(a_n:n≥k)$, then for any sequence $(f_n:n≥1)$ of real numbers satisfying the divide-and-conquer recurrence $f_n = (k-mod(n,k))f_⌊n/k⌋+mod(n,k)f_⌈n/k⌉ + a_n, n ≥k$, there is a unique continuous periodic function $f^*:\mathbb{R}→\mathbb{R}$ with period 1 such that $f_n = nf^*(\log _kn)+o(n)$. If $(a_n)$ is periodic with period $k, a_k=0$, and the initial conditions $(f_i:1 ≤i ≤k-1)$ are all zero, we obtain a specific iterated function system $S$, consisting of $k$ continuous functions from $[0,1]×\mathbb{R}$ into itself, such that the attractor of $S$ is $\{(x,f^*(x)): 0 ≤x ≤1\}$. Using the system $S$, an accurate plot of $f^*$ can be rapidly obtained.
Extending an idea of Suppakitpaisarn, Edahiro and Imai, a dynamic programming approach for computing digital expansions of minimal weight is transformed into an asymptotic analysis of minimal weight expansions. The minimal weight of an optimal expansion of a random input of length $\ell$ is shown to be asymptotically normally distributed under suitable conditions. After discussing the general framework, we focus on expansions to the base of $\tau$, where $\tau$ is a root of the polynomial $X^2- \mu X + 2$ for $\mu \in \{ \pm 1\}$. As the Frobenius endomorphism on a binary Koblitz curve fulfils the same equation, digit expansions to the base of this $\tau$ can be used for scalar multiplication and linear combination in elliptic curve cryptosystems over these curves.