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This paper discusses the balance between artistry and science in the landscape design of memorial gardens, which relies on visual quality prediction. This paper introduces the theoretical basis of vision quality prediction, including the definition, evaluation method and prediction model of vision quality. This paper analyzes the artistry and scientificity of memorial garden landscape design. It expounds that artistry emphasizes the designer’s innovation and aesthetic expression, while scientificity focuses on the feasibility and practicability of design. Finding a balance between the two, so that the design can meet aesthetic and practical needs is an essential challenge for designers. The application of visual quality prediction in memorial garden landscape design and its influence on the balance between artistic and scientific design are discussed in detail. It is found that visual quality prediction can provide a scientific basis for designers to make decisions and help them create high-quality visual effects while meeting practical needs. The research results are summarized, and the future research direction is prospected. With the development of computer technology and artificial intelligence technology, visual quality prediction will play an increasingly important role in landscape design.

Let $\mathrm{\Sigma }=(G,\sigma )$ be a signed graph with a vertex set $V(G)$. A set $D\subseteq V(G)$ is said to be a double dominating set of $\mathrm{\Sigma }$ if it satisfies the following conditions: (i) $|N[v]\cap D|\ge 2$ for each $v\in V(G)$, and (ii) $\mathrm{\Sigma }[D,D^c]$ is balanced, where $N[v]$ denotes the closed neighborhood of $v$ and $\mathrm{\Sigma }[D,D^c]$ denotes the subgraph induced by the edges of $\mathrm{\Sigma }$ with one end vertex in $D$ and the other end vertex in $D^c$. The minimum size among all the double dominating sets of $\mathrm{\Sigma }$ is the double domination number ${\gamma }_{\times 2}(\mathrm{\Sigma })$ of $\mathrm{\Sigma }$. In this study, we investigated this parameter for signed complete graphs. We prove that, for $n\ge 5$, if $(K_n,\sigma )$ is a signed complete graph, then $2\le {\gamma }_{\times 2}(K_n,\sigma )\le n-1$ and these bounds are sharp. Moreover, for all signed complete graphs over $K_n$ we determined their possible double domination numbers. Finally, we compute the double domination numbers of all signed complete graphs of orders up to six.

The prosthetic foot is an essential component of transtibial prosthesis whose mechanical properties affect the balance and gait function. The objective of this study is to examine and compare the biomechanical factors of prosthetic gait and balance for low-cost Ranger foot and somewhat comparatively expensive dynamic response (DR) foot most commonly used in developing countries. Thirty-six subjects with unilateral traumatic transtibial amputation were analyzed for balance and gait attributes using the HUMAC^Ⓡ Balance and Tilt system and 3D motion analysis system with force platform and high-precision optoelectronic cameras, respectively. The paired $t$-test was used to compare the means for static and dynamic balance variables, stride characteristics, and physiological cost index with the $p$-value set as 0.05 for statistical significance. The results revealed that the prosthetic foot design affects the overall balance performance and gait attributes including the physiological energy cost. The DR foot performed better than the Ranger foot in terms of stride characteristics and energy consumption with a significant difference ($p<0.05$) except for the mean walking velocity ($p=0.055$). However, with no articulation at the ankle joint, the Ranger foot improved balance scores with increased stability score ($p=0.0003$), minimizing the excursion of CoP and reducing path length and average velocity. Therefore, the use of Ranger and low-profile DR multiflex feet should be encouraged in the transitory and definitive transtibial prosthetic rehabilitations, respectively, considering the dual advantages of balance and gait attributes.

The purpose of this study was to assess the effect of 18-week Tai Chi training on body balance in dynamic trial among elderly men. The study covered 49 subjects from age 60 to 82.1 years, who had osteopenia or osteoporosis. The subjects were recruited from the community by direct mailings and community efforts to participate in studies. The participants were randomly assigned to either the exercise intervention (n = 25) or control groups (n = 24). The Tai Chi group participated in an 18-week exercise class held for 45 min, twice a week. Body balance was assessed using a Computer Posturographic System PE 90 produced by the Military Institute of Aviation Medicine in Warsaw with modified software made in Pro-Med. During the measurement of body balance, the capacity to perform specific tasks was analyzed (deflections in the set scope and direction). In the Tai Chi group, an increase (p ≤ 0.01) in effectiveness of balance task performance was noted from 80.95% to 84.45% after the training. In the control group, no statistically significant improvement in the level of body balance was found in the same period. Thus, an 18-week period of Tai Chi exercises twice a week for 45 min is beneficial for dynamic balance. It can be important for reducing fall risk factors.

Balance ability decreases with age, which results in an increased risk of falls for people over age 65. Tai Chi exercise appears to offer potential benefits in the reduction of falls for the elderly. The purpose of the present study was to examine the effects of extended (6- and 12-month) Tai Chi exercise interventions on balance and selected motor functions for senior citizens. Forty-seven subjects were recruited from two local senior centers. Twenty of them (M = 71.8 years, SD = 7.1), 11 in the Tai Chi exercise group and 9 in the control group, completed the pre-, mid- and post-tests over 12 months on five selected functional performance tests: static balance, dynamic balance, choice reaction time, heel-rise strength, and ankle flexibility. The Tai Chi group was provided with a one-hour Tai Chi exercise session per week for 12 months; the control group did not participate in any exercise program. Results showed that static balance improved significantly after a 6-month Tai Chi intervention. Moreover, the Tai Chi group maintained a higher level in the test performance compared with the control group at the end of the 12-month intervention, but there was no significant difference between the two groups. Data suggested that Tai Chi exercise intervention could produce a positive influence on balance control for the elderly over a prolonged period, but not on muscle strength and ankle flexibility.

We performed a systematic review of studies regarding the effects of Tai Chi on the body balance of people older than 60 years. The Medline, SPORTDiscus and Academic Search Complete databases were searched for relevant studies published after the year 2000. Original randomized controlled trials, non-randomized controlled studies and observational studies were included in this review if they evaluated Tai Chi for the treatment of body balance disorder or fall prevention, and if they contained at least one of the following key words: Tai Chi, body balance, stability, elderly, old, training or posturography. These studies suggest that participation in Tai Chi may improve the body balance of elderly people; however, more information is needed to determine the extent to which Tai Chi is more effective than other methods, especially different types of physical exercise. In addition, subgroup analyses should be performed to determine the effects of Tai Chi in people with different physical characteristics. Directions for future research are discussed.

The purpose of the present study was to examine the effects of long-term Tai Chi practice on postural balance and H-reflex. Sixteen healthy volunteers, eight with three or more years of experience in Tai Chi training (Tai Chi Group-TCG), and eight with no experience in Tai Chi training (Control Group-CG) participated in the study. Postural sways were measured under four experimental conditions: (1) Standing still with eyes open (EO); (2) Standing still with eyes closed (EC); (3) Standing and turning head to left and right with eyes open (EOT); and (4) Standing and turning head to left and right with eyes closed (ECT). Paired reflex depression (PRD) of the soleus muscle was measured under two conditions: supine and standing. Less significant postural sway was observed in the TCG than in the CG under four conditions including EO, EC, EOT, and ECT (p < 0.01). The TCG demonstrated 14.1%, 30.6%, 33.3% and 22.7% less postural sway, respectively. Significant PRD change from a supine to standing position was observed between TCG and CG (p < 0.05). A significant correlation between PRD change (from supine to standing) and years of Tai Chi practice was observed (r = 0.80, p < 0.05). The findings of this study support the positive effects of Tai Chi exercise on balance control under different conditions. Long-term Tai Chi exercisers also demonstrated different reflex modulation from a supine to standing position, and long-term Tai Chi practice may lead to a change of PRD modulation as neuroadaptation.

Physical limitations, depression and anxiety are prevalent among older adults. Mild to moderate exercise can promote physical and psychological health and reduce the risk of chronic diseases. Qigong, a type of Chinese traditional medicine exercise, has demonstrated beneficial effects on physical ability and mental health in adults with chronic conditions. The purpose of this review was to systematically assess the effects of Qigong exercise on physical and psychological health outcomes in older adults. A total of 1282 older adults aged 62 to 83 years with depressive symptoms, frailty or chronic medical illnesses were included in this review. The meta-analysis showed that Qigong exercise resulted in significantly improved physical ability compared with active control or usual care (standardized mean difference [SMD] $=$ 1.00 and 1.20, respectively). The pooled effects of studies with thrice weekly Qigong sessions had the greatest effect ($\mathrm{\text{SMD}}=1.65$) on physical ability in older adults. Lower quality studies demonstrated larger effect sizes than those of higher quality. Although Qigong exercise showed favorable effects on depression, balance and functioning, the overall effects did not reach statistical significance. No significant adverse events were reported. The findings suggest that the Qigong exercise may be an option for older adults to improve physical ability, functional ability, balance and to lessen depression and anxiety. However, the number of RCTs that enroll older adults is limited. More methodologically sound RCTs are needed to confirm the efficacy of Qigong exercise on physical and psychological health in older adults with chronic illnesses.

Equivariant dynamical systems possess canonical flow-invariant subspaces, the fixed-point spaces of subgroups of the symmetry group. These subspaces classify possible types of symmetry-breaking. Coupled cell networks, determined by a symmetry groupoid, also possess canonical flow-invariant subspaces, the balanced polydiagonals. These subspaces classify possible types of synchrony-breaking, and correspond to balanced colorings of the cells. A class of dynamical systems that is common to both theories comprises networks that are symmetric under the action of a group Γ of permutations of the nodes ("cells"). We investigate connections between balanced polydiagonals and fixed-point spaces for such networks, showing that in general they can be different. In particular, we consider rings of ten and twelve cells with both nearest and next-nearest neighbor coupling, showing that exotic balanced polydiagonals — ones that are not fixed-point spaces — can occur for such networks. We also prove the "folk theorem" that in any Γ-equivariant dynamical system on R^k the only flow-invariant subspaces are the fixed-point spaces of subgroups of Γ.

This paper continues the study of patterns of synchrony (equivalently, balanced colorings or flow-invariant subspaces) in symmetric coupled cell networks, and their relation to fixed-point spaces of subgroups of the symmetry group. Our aim is to provide a group-theoretic explanation of the "exotic" balanced coloring previously discussed in Part 2. Here we show that the pattern can be obtained as a projection into two dimensions of a fixed-point pattern in a three-dimensional lattice. We prove a general theorem giving sufficient conditions for such a construction to lead to a balanced coloring, for an arbitrary direct product of group networks.

Following Golubitsky, Stewart, and others, we give definitions of networks and input trees. In order to make our work as general as possible, we work with a somewhat extended notion of multiplicity, and introduce the concept of "bunching" of trees. We then define balanced equivalence relations on networks, and a partial ordering on these relations. Previous work has shown that there is a maximal balanced equivalence relation on networks of certain classes: we provide a different style of proof which gives this result for any network. We define two algorithms to determine this relation in practice on a given finite network — one for use with networks with all multiplicities equal, and a second for the more general case. We then provide illustrative examples of each algorithm in use. We show both of these algorithms to be quartic in the size of the given network.

Balanced colorings of networks correspond to flow-invariant synchrony spaces. It is known that the coarsest balanced coloring is equivalent to nodes having isomorphic infinite input trees, but this condition is not algorithmic. We provide an algorithmic characterization: two nodes have the same color for the coarsest balanced coloring if and only if their $(n-1)$th input trees are isomorphic, where $n$ is the number of nodes. Here $n-1$ is the best possible. The proof is analogous to that of Leighton’s theorem in graph theory, using the universal cover of the network and the notion of a symbolic adjacency matrix to set up a partition refinement algorithm whose output is the coarsest balanced coloring. The running time of the algorithm is cubic in $n$.

Purpose: To evaluate and to find an association between postural stability amongst the subjects with sacroiliac iliac joint pain (SIJP) and compare it with healthy subjects. Methods: Single leg standing balance test with eyes closed (SLSBT-EC) was performed in 30 SIJP subjects without any visual, vestibular or other neuromusculoskeletal conditions and in 46 healthy controls aged 18-59 years. SLSBT-EC holding duration was measured for both the groups. "t"-test was done to compare the SLSBT (EC) holding duration between the groups and Fisher's exact test to find an association between postural stability and SIJP group. Results: SLSBT (EC) duration was significantly decreased (95% CI: t = 10.34, p = < 0.001) amongst the cases (15.56 s ± 4.73 s) as compared to healthy participants (26.06 s ± 4.05 s) and Fisher's exact test value for association between postural stability and SIJP was found to be statistically significant (F = 0.54, p = < 0.001). Conclusion: Subjects with SIJP exhibited diminished SLSBT (EC) holding duration compared to healthy controls suggesting proprioceptive deficits.

A Signed graph (or sigraph in short) is an ordered pair S = (G, σ), where G is a graph G = (V, E) and σ : E → {+, −} is a function from the edge set E of G into the set {+, −}. For a positive integer n > 1, the unitary Cayley graph X_n is the graph whose vertex set is Z_n, the integers modulo n and if U_n denotes set of all units of the ring Z_n, then two vertices a, b are adjacent if and only if a − b ∈ U_n. In this paper, we have obtained a characterization of balanced and clusterable unitary Cayley ring sigraph . Further, we have established a characterization of canonically consistent unitary Cayley ring sigraph , where n has at most two distinct odd primes factors. Also sign-compatibility has been worked out for the same.

We introduce and investigate in this paper a kind of Tate homology of modules over a commutative coherent ring based on Tate ℱ_C-resolutions, where C is a semidualizing module. We show firstly that the class of modules admitting a Tate ℱ_C-resolution is equal to the class of modules of finite 𝒢(ℱ_C)-projective dimension. Then an Avramov–Martsinkovsky type exact sequence is constructed to connect such Tate homology functors and relative homology functors. Finally, motivated by the idea of Sather–Wagstaff et al. [Comparison of relative cohomology theories with respect to semidualizing modules, Math. Z. 264 (2010) 571–600], we establish a balance result for such Tate homology over a Cohen–Macaulay ring with a dualizing module by using a good conclusion provided in [E. E. Enochs, S. E. Estrada and A. C. Iacob, Balance with unbounded complexes, Bull. London Math. Soc. 44 (2012) 439–442].

Let $R$ be an arbitrary ring. We use a strict ${𝒲}{𝒳}$-resolution $X$ of a complex $K$ with finite $\widetilde{\#\mathrm{\text{-}}{𝒳}}$-projective dimension, where ${𝒳}$ denotes a subcategory of right $R$-modules closed under extensions and direct summands and admits an injective cogenerator ${𝒲}$, to define the $n$th relative cohomology functor ${\mathrm{\text{Ext}}}_{{𝒳}C}^n(K,-)$ as ${\mathrm{\text{H}}}^{-n}{\mathscr{H}}\mathrm{\text{om}}(X,-)$. If a complex $L$ has finite $\widetilde{\#\mathrm{\text{-}}{𝒴}}$-injective dimension, then one can use a dual argument to define a notion of a relative cohomology functor ${\mathrm{\text{Ext}}}_{{𝒞}Y}^n(-,L)$, where ${𝒴}$ is a subcategory of right $R$-modules closed under extensions and direct summands and admits a projective generator. Under several orthogonal conditions, we show that there exists an isomorphism ${\mathrm{\text{Ext}}}_{{{𝒳}C}^n}(K,L)\cong {\mathrm{\text{Ext}}}_{{𝒞}{𝒴}}^n(K,L)$ of relative cohomology groups for each $n\in \mathbb{Z}$. This result simultaneously encompasses a balance result of Holm on Gorenstein projective and injective modules, a balance result of Sather-Wagstaff, Sharif and White on Gorenstein projective and injective modules with respect to semidualizing modules, and a balance result of Liu on Gorenstein projective and injective complexes. In particular, as an application of this result, we extend the above balance result of Sather-Wagstaff, Sharif and White to the setting of complexes.

Let $X$ and $Y$ be $N$-complexes with $N\ge 2$ an integer such that $X$ has finite Gorenstein projective dimension and $Y$ has finite Gorenstein injective dimension. We define the $n$th Gorenstein cohomology groups

Impaired balance is one of the most disabling multiple sclerosis (MS) symptoms. It is known that, in the presence of predictable perturbations, the central nervous system (CNS) utilizes both anticipatory (APAs) and compensatory (CPAs) postural adjustments to maintain balance. The main purpose of this study was to investigate the relationship between APAs and CPAs during self-induced postural perturbation in patients with MS. Participants performed a load release task while standing on a force platform. Electrical activity of six leg and trunk muscles, as well as displacements of the center of pressure (COP), was recorded. The results revealed significant APAs deficits in MS patients reflected in short APAs duration and reduced magnitude. The reduced APAs were not accompanied by significant compensatory muscle activity. It can be concluded that there is an impairment of feed-forward postural control in MS, and feedback-based mechanisms (CPAs) are unable to compensate for these APA deficits. These results should be considered in the rehabilitation programs for balance training of MS patients.

Although a significant amount of research has examined the biomechanical effects of carrying a load on human walking, most has focussed on fore and aft loads, or evenly balanced loads. In addition, most research on human walking no longer considers footprint analysis, despite its ease of use and its effectiveness in studies of balance. However, one project, with a small number of subjects, suggested that people carrying a heavy load in one hand (e.g., a suitcase or toolbox) make two sorts of adjustments to the placement of their feet on the substrate. The first and most obvious change is a decrease in foot angle (in-toeing) on the unloaded side. This puts the anterior part of the foot further under the center of mass when carrying a load in the contralateral hand and has been amply documented in subsequent studies. The second and more subtle change is a decrease in step width, a practice which also moves the foot on the unloaded side closer to the center of mass. However, tests subsequent to the original study did not show a consistent or significant use of this technique. This discrepancy between original and subsequent results in step width can be explained by the level of expertise which various subjects have. Experience carrying heavy loads may be required for most subjects to develop ways of accommodating loads. For this project, subjects were tested under two conditions: carrying an empty canvas bag; carrying the same bag with 21% of their body weight in it. All subjects walked on paper runners, wearing paint-soaked socks to leave footprint trails. Subjects were asked to walk once with no weights followed by three more times with weights. They were then given 10–15min of practice with the weighted bag, then asked to repeat the protocol, for a total of eight trials (two unweighted and six weighted). Foot angle and step width were measured for all trials. Results show that practice does indeed make a difference in the use of a narrower step when carrying a heavy load. Specifically, the first three weighted trials show a decrease in step width that is nonsignificant, but the last three evince a significant reduction as compared to unweighted trials. In addition, lifetime experience carrying a heavy load led to more immediate changes in foot placement. We conclude that the initial study involved subjects who already had experience carrying a unilateral heavy load and that, as with other activities, mechanically more effective movements are acquired with greater experience and practice.

Background: Recently, new methods have emerged that encourage voluntary participation by allowing patients to perform tasks, including exercises or treatments, in a virtual reality (VR) environment. Aim: This study aimed to examine the effects of full immersion virtual reality training on balance and knee function in patients who had undergone total knee replacement. Design: Single blind randomized controlled trial. Setting: Department of Physical Therapy in a rehabilitation center. Population: A total of 30 elderly patients ($\ge$65 years old) who had undergone total knee replacement. Methods: Participants were randomly allocated to an experimental group ($n=18$) and a control group ($n=18$). The experimental group received with a continuous passive motion machine, exercise therapy, and a full immersion VR training program; the control group received only with a continuous passive motion machine and exercise therapy. Biorescue was used to test static and dynamic balance ability, and the Timed Up and Go and Western Ontario and McMaster Universities tests were used to assess knee function. Paired $t$-tests were used to examine differences by time in each group, and independent $t$-tests were used to examine differences between the groups. Results: In terms of within-group differences by time, both the experimental group and the control group showed significant changes in the anterior, and posterior limits of stability in both sides; static balance; and knee function. In the between-groups comparison, among static balance tests, there was a significant difference in center of mass path length in the standing position with eyes open ($p=0.006$); among dynamic balance tests, there were significant differences in left, right, anterior, and posterior limits of stability ($p=0.00$). Conclusions: VR training produced better early balance ability and knee function than what was seen in the control group. We believe that VR training in initial post-operative rehabilitation of total knee replacement patients may increase the rate of recovery. Clinical Rehabilitation Impact: VR exercise programs are effective in early rehabilitation after total knee replacement, and have clinical value as inexpensive methods that can promote active participation.