scholarly journals On a Recurrence Arising in Graph Compression

10.37236/2540 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Yongwook Choi ◽  
Charles Knessl ◽  
Wojciech Szpankowski
Keyword(s):  
Nonnegative Integer ◽  
Path Length ◽  
Compression Algorithm ◽  
Simple Rule ◽  
Mellin Transforms ◽  
Graph Compression ◽  
The Right

In a recently proposed graphical compression algorithm by Choi and Szpankowski (2012), the following tree arose in the course of the analysis. The root contains $n$ balls that are consequently distributed between two subtrees according to a simple rule: In each step, all balls independently move down to the left subtree (say with probability $p$) or the right subtree (with probability $1-p$). A new node is created as long as there is at least one ball in that node. Furthermore, a nonnegative integer $d$ is given, and at level $d$ or greater one ball is removed from the leftmost node before the balls move down to the next level. These steps are repeated until all balls are removed (i.e., after $n+d$ steps). Observe that when $d=\infty$ the above tree can be modeled as a trie that stores $n$ independent sequences generated by a binary memoryless source with parameter $p$. Therefore, we coin the name $(n,d)$-tries for the tree just described, and to which we often refer simply as $d$-tries. We study here in detail the path length, and show how much the path length of such a $d$-trie differs from that of regular tries. We use methods of analytic algorithmics, from Mellin transforms to analytic poissonization.

scholarly journals A New Binomial Recurrence Arising in a Graphical Compression Algorithm

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Yongwook Choi ◽  
Charles Knessl ◽  
Wojciech Szpankowski
Keyword(s):  
Nonnegative Integer ◽  
Path Length ◽  
Compression Algorithm ◽  
Simple Rule ◽  
Two Dimensional ◽  
Mellin Transforms ◽  
International Audience ◽  
The Right

International audience In a recently proposed graphical compression algorithm by Choi and Szpankowski (2009), the following tree arose in the course of the analysis. The root contains n balls that are consequently distributed between two subtrees according to a simple rule: In each step, all balls independently move down to the left subtree (say with probability $p$) or the right subtree (with probability 1-$p$). A new node is created as long as there is at least one ball in that node. Furthermore, a nonnegative integer $d$ is given, and at level $d$ or greater one ball is removed from the leftmost node before the balls move down to the next level. These steps are repeated until all balls are removed (i.e., after $n+d$ steps). Observe that when $d=∞$ the above tree can be modeled as a $\textit{trie}$ that stores $n$ independent sequences generated by a memoryless source with parameter $p$. Therefore, we coin the name $(n,d)$-tries for the tree just described, and to which we often refer simply as $d$-tries. Parameters of such a tree (e.g., path length, depth, size) are described by an interesting two-dimensional recurrence (in terms of $n$ and $d$) that – to the best of our knowledge – was not analyzed before. We study it, and show how much parameters of such a $(n,d)$-trie differ from the corresponding parameters of regular tries. We use methods of analytic algorithmics, from Mellin transforms to analytic poissonization.

Leaky integration during blindfolded walking along veering paths

2012 ◽  
Vol 25 (0) ◽  
pp. 139
Author(s):  
Markus Lappe ◽  
Claudia Fontaine ◽  
Harald Frenz
Keyword(s):  
Path Integration ◽  
Path Length ◽  
Distance Estimation ◽  
Forward Direction ◽  
Travel Distance ◽  
Integration Model ◽  
Starting Point ◽  
End Distance ◽  
Leaky Integration ◽  
The Right

We compare travel distance estimation from path integration during walking with path integration from visual flow. For visually simulated self-movement humans typically underestimate travel distance, which can be explained by leaky path integration. The amount of leak, i.e., the underestimation, is determined by the length of the path. For visually simulated movements along curved paths that veer left and right around a central forward direction estimates of the start-to-end distance decrease as the veering, i.e., the path length increases. Leaky path integration for visual travel distance estimation thus takes place along the actually traversed path even when a straight beeline distance is calculated. We studied whether the same leaky path integration occurs during real self-motion when vestibular and proprioceptive cues are available instead of vision. Sixteen subjects walked blindfolded from a starting point to targets 20, 30 or 40 m away, guided by an experimenter. They walked either along a straight line, or along paths that deviated first to the right and then to the left (or vice versa) before they reached the end point. This increased the path length by 5, 10, 20 or 30%. Subjects then gave a verbal estimate of their beeline distance from the starting point. Like in the visually simulated case, distance estimates for the same start-to-end distance of 40 m dropped as the path length increased, consistent with the prediction of the leaky integration model. We conclude that travel distance estimation is similar for visual and for vestibular/proprioceptive cues.

scholarly journals Assessment of Postural Balance in Women Treated for Breast Cancer

Medicina ◽  
2020 ◽  
Vol 56 (10) ◽  
pp. 505
Author(s):  
Iwona Głowacka-Mrotek ◽  
Magdalena Tarkowska ◽  
Tomasz Nowikiewicz ◽  
Magdalena Hagner-Derengowska ◽  
Aleksander Goch
Keyword(s):  
Breast Cancer ◽  
Postural Balance ◽  
Path Length ◽  
Muscle Tension ◽  
The Body ◽  
Control Group ◽  
Foot Pressure ◽  
Static Test ◽  
Healthy Female ◽  
The Right

Background and objectives: Surgery is the primary and most effective treatment of breast cancer. Unilateral mastectomy disrupts the distribution of muscle tension between the right and the left sides of the body. The aim of the study was to evaluate postural balance in patients treated for breast cancer by mastectomy. Materials and methods: A controlled clinical study was conducted on 90 patients who have undergone surgical treatment for breast cancer (mastectomy) 5–6 years prior (Breast Group—BG). The control group (CG) consisted of 74 healthy female volunteers. Analysis of balance was performed using the Alfa stabilography platform. A static test (Romberg’s test) with open and closed eyes was used to assess balance. The following balance parameters were analyzed: path length, statokinesigram area, parameters of deflection and velocity of the foot pressure center. Results: The study demonstrated that patients from BG (5–6 years after surgery) obtained worse results in both tests with open (maximum back deviation, maximum forward deviation, average Y deviation, average Y velocity, path length and path surface area) (p < 0.05) as well as with closed eyes (maximum backward deviation, maximum forward deviation, mean Y deviation and path length) (p < 0.05). Conclusions: Our study demonstrated that women 5–6 years after surgery for breast cancer have impaired balance compared to healthy women, despite physiotherapy.

scholarly journals Top Coefficients of the Denumerant

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Velleda Baldoni ◽  
Nicole Berline ◽  
Brandon Dutra ◽  
Matthias Köppe ◽  
Michele Vergne ◽  
...  
Keyword(s):  
Nonnegative Integer ◽  
Fixed Number ◽  
Lattice Points ◽  
Combinatorial Number Theory ◽  
International Audience ◽  
Integer Solutions ◽  
Combinatorial Function ◽  
Rational Generating Function ◽  
Rational Generating Functions ◽  
The Right

International audience For a given sequence $\alpha = [\alpha_1,\alpha_2,\ldots , \alpha_N, \alpha_{N+1}]$ of $N+1$ positive integers, we consider the combinatorial function $E(\alpha)(t)$ that counts the nonnegative integer solutions of the equation $\alpha_1x_1+\alpha_2 x_2+ \ldots+ \alpha_Nx_N+ \alpha_{N+1}x_{N+1}=t$, where the right-hand side $t$ is a varying nonnegative integer. It is well-known that $E(\alpha)(t)$ is a quasipolynomial function of $t$ of degree $N$. In combinatorial number theory this function is known as the $\textit{denumerant}$. Our main result is a new algorithm that, for every fixed number $k$, computes in polynomial time the highest $k+1$ coefficients of the quasi-polynomial $E(\alpha)(t)$ as step polynomials of $t$. Our algorithm is a consequence of a nice poset structure on the poles of the associated rational generating function for $E(\alpha)(t)$ and the geometric reinterpretation of some rational generating functions in terms of lattice points in polyhedral cones. Experiments using a $\texttt{MAPLE}$ implementation will be posted separately. Considérons une liste $\alpha = [\alpha_1,\alpha_2,\ldots , \alpha_N, \alpha_{N+1}]$ de $N+1$ entiers positifs. Le dénumérant $E(\alpha)(t)$ est lafonction qui compte le nombre de solutions en entiers positifs ou nuls de l’équation $\sum^{N+1}_{i=1}x_i\alpha_i=t$, où $t$ varie dans les entiers positifs ou nuls. Il est bien connu que cette fonction est une fonction quasi-polynomiale de $t$, de degré $N$. Nous donnons un nouvel algorithme qui calcule, pour chaque entier fixé $k$ (mais $N$ n’est pas fixé, les $k+1$ plus hauts coefficients du quasi-polynôme $E(\alpha)(t)$ en termes de fonctions en dents de scie. Notre algorithme utilise la structure d’ensemble partiellement ordonné des pôles de la fonction génératrice de $E(\alpha)(t)$. Les $k+1$ plus hauts coefficients se calculent à l’aide de fonctions génératrices de points entiers dans des cônes polyèdraux de dimension inférieure ou égale à $k$.

scholarly journals Connectivity modulations induced by reach&grasp movements: a multidimensional approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Pietro Caliandro ◽  
Gloria Menegaz ◽  
Chiara Iacovelli ◽  
Carmela Conte ◽  
Giuseppe Reale ◽  
...  
Keyword(s):  
Path Length ◽  
Movement Time ◽  
Insular Cortex ◽  
Arm Movement ◽  
Global Efficiency ◽  
Brodmann Areas ◽  
Topological Measures ◽  
Measuring Network ◽  
The Right ◽  
Complex Architecture

AbstractReach&grasp requires highly coordinated activation of different brain areas. We investigated whether reach&grasp kinematics is associated to EEG-based networks changes. We enrolled 10 healthy subjects. We analyzed the reach&grasp kinematics of 15 reach&grasp movements performed with each upper limb. Simultaneously, we obtained a 64-channel EEG, synchronized with the reach&grasp movement time points. We elaborated EEG signals with EEGLAB 12 in order to obtain event related synchronization/desynchronization (ERS/ERD) and lagged linear coherence between Brodmann areas. Finally, we evaluated network topology via sLORETA software, measuring network local and global efficiency (clustering and path length) and the overall balance (small-worldness). We observed a widespread ERD in α and β bands during reach&grasp, especially in the centro-parietal regions of the hemisphere contralateral to the movement. Regarding functional connectivity, we observed an α lagged linear coherence reduction among Brodmann areas contralateral to the arm involved in the reach&grasp movement. Interestingly, left arm movement determined widespread changes of α lagged linear coherence, specifically among right occipital regions, insular cortex and somatosensory cortex, while the right arm movement exerted a restricted contralateral sensory-motor cortex modulation. Finally, no change between rest and movement was found for clustering, path length and small-worldness. Through a synchronized acquisition, we explored the cortical correlates of the reach&grasp movement. Despite EEG perturbations, suggesting that the non-dominant reach&grasp network has a complex architecture probably linked to the necessity of a higher visual control, the pivotal topological measures of network local and global efficiency remained unaffected.

scholarly journals Assessment of the Relationship between Y-Balance Test and Stabilometric Parameters in Youth Footballers

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Damian Sikora ◽  
Małgorzata Pałac ◽  
Andrzej Myśliwiec ◽  
Tomasz Wolny ◽  
Paweł Linek
Keyword(s):  
Path Length ◽  
Dynamic Balance ◽  
Dynamic Test ◽  
Lower Limbs ◽  
Test Results ◽  
Dynamic Tests ◽  
Balance Test ◽  
Time Required ◽  
The Right ◽  
The Relationship

Objectives. The purpose of the study was to evaluate the correlation between dynamic test results obtained on a stabilometric platform and the results achieved on the Y-balance test (Y-BT). Method. The study group consisted of 52 adolescent athletes, aged 14 to 17 years. Each participant was evaluated in the scope of their ability to maintain dynamic balance using the Y-BT as well as via dynamic tests on the ‘Alfa’ stabilometric platform. The following parameters were analysed: (a) from the Y-BT—relative reach of the right and left lower limbs in the anterior, posterolateral, and posteromedial directions, as well as the side-to side difference in relative reach for each direction and (b) from the ‘Alfa’ platform—path length and time to reach the target using right and left lower limbs in the anterior and posterior directions. Results. A correlation between the results obtained on the stabilometric platform and the Y-BT was found only for the posteromedial direction. Statistical analysis demonstrated that the increased difference between the right and left lower limbs in the posteromedial test is related to an increase in time taken to reach the points located forward and to the left, and backwards and to the right, as well as an increase in the overall time required to complete the task on the stabilometric platform. Conclusions. The results from the Y-BT and stabilometric platform are weakly related in adolescents. These findings indicate that the Y-BT and stabilometric platform analyse different kinds of dynamic balance in adolescents. Thus, these tools should not be used interchangeably in clinical practice or scientific research.

Memory for Reward in Probabilistic Choice: Markovian and Non-Markovian Properties

Behaviour ◽  
1990 ◽  
Vol 114 (1-4) ◽  
pp. 37-64 ◽  
Author(s):  
J.E.R. Staddon ◽  
Derick G.S. Davis
Keyword(s):  
Linear Model ◽  
Spontaneous Recovery ◽  
Simple Rule ◽  
Experimental Session ◽  
Probabilistic Choice ◽  
Left Response ◽  
Reminiscence Effect ◽  
The Right ◽  
Longterm Memory ◽  
Memory Parameter

AbstractPigeons were rewarded with food for pecking keys in various forms of two-armed bandit situation for an extended series of daily sessions in two experiments. The average daily preference (S=R/[R+L]) is very well fit by a markovian linear model in which predicted preference today is an average of predicted preference yesterday and reinforcement conditions today: s(N+1) = as(N) + (1-a)A(N+1), where A(N+1) is set equal to 1 when all rewards are for the Right response, and 0 when all are for the Left, and a is a longterm memory parameter. This linear model explains some apparent paradoxes in earlier reports of memory effects in two-armed bandit experiments. Nevertheless, closer examination of the details of preference changes within each experimental session showed several kinds of non-markovian effects. The most important was a regression at the beginning of each experimental session towards a preference characteristic of earlier sessions (spontaneous recovery). This effect, but not a smaller, less reliable non-markovian reminiscence effect, is consistent with a very simple rule, namely that the effect on preference of each individual reward for a Right or Left response is inversely related to how long ago the reward occurred. Thus, animals learn to prefer the rewarded side each day because these rewards are recent; but they regress to earlier preferences overnight because the most recent rewards become relatively less recent with lapse of time.

scholarly journals The Role of Simulator Promis2 in Learning Laparoscopic Skill

2009 ◽  
Vol 48 (175) ◽  
Author(s):  
Suman K Shrestha ◽  
T Nomura ◽  
T Tajiri ◽  
I Akagi ◽  
R Aso ◽  
...  
Keyword(s):  
Path Length ◽  
Simulator Training ◽  
Laparoscopic Skill ◽  
Laparoscopic Skills ◽  
Left Hand ◽  
Left Handed ◽  
Path Lengths ◽  
The Right ◽  
Right And Left Hand

Introduction: Laparoscopic surgery is unique and complex in nature, so the training is necessarybefore proceeding to operation room. Many computer aided simulators have been developed forthe purpose. Our objective is to assess the improvement of basic laparoscopic skills after training insimulator.Methods: The fi fth year medical students underwent training of three laparoscopic skills usingPromis2 simulator twice weekly for 4-6 weeks. The skills are laparoscopic orientation, target pointingand objects transferring. Time, path length of instruments and economy of movements were recorded.The comparisons were made for these parameters between session fi rst and the last using a Mann-Whitney U test.Results: Ten volunteers completed the exercises in less time (186.3±55.4 seconds) than the fi rstexercise (215.7±57.4 seconds) (P=0.0027). Both the right and left hand instrument path lengths werealso improved from 4425.8±1284.3 mm in the fi rst exercise to 3925.3±1313.6 mm in the last exercisein the left side (P=0.0219) and likewise from 4273.8±1859.4 mm to 3831.3±1717.4 mm in the right side(P=0.0027). Economy of the movement in the left handed instrument improved from 1114.4±453.5mm in the fi rst exercise to 966.8±411.1 mm in the last (P=0.0443) and in the right handed instrumentfrom 845±398.8 mm to 771.4±370.5 mm according to the software of Promis2 simulator (P >0.005).Conclusions: Training in Promis2 simulator improves the basic laparoscopic skills. The candidatesbecome consistently faster with shorter path lengths and had smoother instruments movements.They also became signifi cantly more consistent in their performance.Key Words: laparoscopy, promis2, simulator, training

scholarly journals Disrupted Network Topology Contributed to Spatial Navigation Impairment in Patients With Mild Cognitive Impairment

2021 ◽  
Vol 13 ◽  
Author(s):  
Weiping Li ◽  
Hui Zhao ◽  
Zhao Qing ◽  
Zuzana Nedelska ◽  
Sichu Wu ◽  
...  
Keyword(s):  
Cognitive Impairment ◽  
Mild Cognitive Impairment ◽  
Shortest Path ◽  
Network Topology ◽  
Path Length ◽  
Spatial Navigation ◽  
Structural Connectivity ◽  
Clustering Coefficient ◽  
Topological Features ◽  
The Right

Impairment in spatial navigation (SN) and structural network topology is not limited to patients with Alzheimer’s disease (AD) dementia and can be detected earlier in patients with mild cognitive impairment (MCI). We recruited 32 MCI patients (65.91 ± 11.33 years old) and 28 normal cognition patients (NC; 69.68 ± 10.79 years old), all of whom underwent a computer-based battery of SN tests evaluating egocentric, allocentric, and mixed SN strategies and diffusion-weighted and T1-weighted Magnetic Resonance Imaging (MRI). To evaluate the topological features of the structural connectivity network, we calculated its measures such as the global efficiency, local efficiency, clustering coefficient, and shortest path length with GRETNA. We determined the correlation between SN accuracy and network topological properties. Compared to NC, MCI subjects demonstrated a lower egocentric navigation accuracy. Compared with NC, MCI subjects showed significantly decreased clustering coefficients in the left middle frontal gyrus, right rectus, right superior parietal gyrus, and right inferior parietal gyrus and decreased shortest path length in the left paracentral lobule. We observed significant positive correlations of the shortest path length in the left paracentral lobule with both the mixed allocentric–egocentric and the allocentric accuracy measured by the average total errors. A decreased clustering coefficient in the right inferior parietal gyrus was associated with a larger allocentric navigation error. White matter hyperintensities (WMH) did not affect the correlation between network properties and SN accuracy. This study demonstrated that structural connectivity network abnormalities, especially in the frontal and parietal gyri, are associated with a lower SN accuracy, independently of WMH, providing a new insight into the brain mechanisms associated with SN impairment in MCI.

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