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| 1 | Correlation between muscular strength and basal nuclei ischemic/hemorrhagic stroke-induced corticospinal tract injury,as detected by diffusion tensor imaging and tractography显示文摘BACKGROUND:Conventional neuroimaging diagnosis does not assist with the monitoring or evaluation of basal nuclei ischemic and hemorrhagic stroke,or motor functional recovery.Magnetic resonance,diffusion tensor imaging,and diffusion tensor tractography have all been used to observe features of cerebral white matter fibrous structures.In addition,diffusion tensor tractography is the only non-invasive imaging method to display the corticospinal tract in vivo.OBJECTIVE:To evaluate the impairment degree of corticospinal tract induced by basal nuclei ischemic and hemorrhagic stroke through the use of magnetic resonance,diffusion tensor imaging,and diffusion tensor tractography,and to analyze the correlation to muscular strength.DESIGN,TIME AND SETTING:A retrospective case analysis was performed at the Department of Medical Imaging,Neurology and Neurosurgery,Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA between November 2002 and June 2008.PARTICIPANTS:A total of 15 patients with acute or subacute cerebral ischemic stroke and nine with hemorrhagic stroke in the basal nuclei were selected.METHODS:Magnetic resonance,diffusion tensor imaging,and diffusion tensor tractography results and data were analyzed.Fractional anisotropy and directionally encoded color maps were obtained.Three-dimensional tractography of bilateral corticospinal tract was created,and corticospinal tract integrity was graded.Fractional anisotropy of infarct region and corresponding contralateral normal regions were measured,and hematoma volume in hemorrhagic stroke patients was determined.Hand motor function ability was evaluated using Brunstorm criteria.MAIN OUTCOME MEASURES:Fractional anisotropy of infarct region and corresponding contralateral normal regions;hematoma volume in hemorrhagic stroke patients;correlation between muscular strength and corticospinal tract impairment degree in ischemic stroke and hemorrhagic stroke patients before and after treatment.RESULTS:In ischemic stroke patients,the fractional anisotropy value was significantly lower in the infarct area of white matter than in the normal hemisphere(P < 0.01).The impairment degree of corticospinal tract negatively correlated with muscular strength of the corresponding hand(r =-0.97 P < 0.01).The hematoma volume of hemorrhagic stroke patients significantly negatively correlated with Spearman test results for muscular strength of the corresponding hand(r =-0.88,P < 0.01).CONCLUSION:Corticospinal tract impairment severity negatively correlated with muscular strength and motor functional recovery,which suggested that diffusion tensor imaging and diffusion tensor tractography could be used to evaluate corticospinal tract motor function. | Shangwen Xu Ziqian Chen Jinhua Chen Youqiang Ye Yuning Lin Ping Ni Hui Xiao Gennian Qian | 2010 | Neural Regeneration Research2010，5，13： | 7 |
| 2 | Evaluating ischemic stroke with diffusion tensor imaging显示文摘Objective:In recent years,diffusion tensor imaging (DTI) has emerged as a promising tool to study ischemic stroke. The aim of this study is to evaluate the anisotropic changes of cerebral white matter tracks in patients with ischemic stroke using DTI,and investigate the correlation between corticospinal tract damage and muscle strength in such patients during acute ischemia.Method:9 patients with acute ischemic stroke and 9 healthy subjects were examined with T1 weighted magnetic resonance imaging (MRI),T2 weighted MRI and DTI. Fractional anisotropy (FA) was measured and the three-dimensional fibrous band images of bilateral corticospinal tracts were reconstructed. The muscle strength of the affected hand was assessed by Brunnstorm standard[1],which is an internationally recognized measure of movement in hemiplegic patients.Results:①In the control group,there was no significant difference in FA between the bilateral corticospinal tracts,but FA in different white matter structure of the same side was significantly different (t=3.12,P < 0.05). FA of posterior limb of internal capsule was higher than that of knee and anterior limb of internal capsule,FA of anterior limb of internal capsule was the lowest. while in the patient group,FA of the infarcted sites was significantly lower than the contralateral ones (t=5.570,P < 0.01). ②The ipsilateral corticospinal tract demonstrated continuous interruption and the loss of consistent anatomic structure. The involved severity of corticospinal tract had significant correlation with that of muscle strength of the ipsilateral hand (r=0.83,P < 0.01).Conclusion:This study shows that DTI can be used to investigate ischemic stroke and assess ischemic stroke-induced damage. The damaged severity of corticospinal tracts is correlated with that of muscle strength. | Ziqian Chen Ping Ni Youqiang Ye Hui Xiao Gennian Qian Shangwen Xu Jingliang Wang Xizhang Yang Jinhua Chen Zhenshan Shi Biyun Zhang | 2008 | 福州总医院学报2008，15，3： | 6 |
| 3 | Construction of optimal supersaturated designs by the packing method显示文摘A supersaturated design is essentially a factorial design with the equal occurrence of levels property and no fully aliased factors in which the number of main efits potential in factor screening experiments. A packing design is an important object in combinatorial design theory. In this paper, a strong link between the two apparently unrelated kinds of designs is shown. Several criteria for comparing supersaturated designs are proposed, their properties and connections with other existing criteria are discussed.A combinatorial approach, called the packing method, for constructing optimal supersaturated designs is presented, and properties of the resulting designs are also investigated.Comparisons between the new designs and other existing designs are given, which show that our construction method and the newly constructed designs have good properties. | FANG Kaitai GE Gennian LIU Minqian | 2004 | Science China Mathematics2004，47，1： | 4 |
| 4 | MRI and diffusion tensor imaging in assessing correlation of activation of cortical motor function and manifestations of corticospinal tract with muscle strength in patients with ischemic stroke显示文摘BACKGROUND: Ischemic stroke is often followed by the abnormalities of neurons and corticospinal tract, which can lead to corresponding clinical symptoms and signs. Recently, with the continuous perfection of high-field MRI instrument, it becomes possible to assess and investigate the cortical function and structural reconstruction following stroke by using MRI and diffusion tensor imaging (DTI). OBJECTIVE: To observe the cortical motor function and changes of corticospinal tracts by using MRI and DTI in the patients with ischemic stroke at acute period, compare with the normal subjects, and assess the damage of corticospinal tract and muscle strength. DESIGN: A case-control observation. SETTING: Department of Medical Imaging, Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA. PARTICIPANTS: Nine inpatients (5 males and 4 females) with injury of motor function induced by acute ischemic stroke were selected from Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA between August and December in 2005, they aged 16-87 years with an average of 51 years old, and those with obvious conscious disturbances and severe cognitive disorders were excluded. At the same time, nine healthy right-handed physical examinees matched by age and gender with the patients were also selected, and they all had no nervous disease, epilepsy, mental diseases, cerebrovascular abnormalities and injury history, etc. All the subjects were informed with the detected items and agreed to participate in. METHODS: All the 9 patients with ischemic stroke at acute period and 9 healthy subjects were examined with MRI and DTI. ① A block-based design was used in the MRI, the passive finger-to-finger exercise was used as the stimulative task, and the static condition was taken as the baseline task. The GE 1.5T MRI system was used, all the data were processed after off-line, and analyzed with the SPM2 software, the association between the activated area and local anatomy of brain was observed. ② The DTI image was processed with the dTV.II.R1 software part of the anisotropic image and color anisotropic image were shown, and the three-dimensional white matter image of bilateral corticospinal tracts of the patients were reconstructed.③ The muscle strength of the affected hand of the stroke patients was judged with the Brunnstorm standard. MAIN OUTCOME MEASURES: The manifestations of MRI, DTI and corticospinal tracts of the 9 stroke patients were mainly observed. RESULTS: All the 9 stroke patients and 9 healthy subjects were involved in the analysis of results. ① Results of MRI examination: The handed exercise of the healthy subjects mainly activated contralateral sensorimotor cortex, posterior parietal cortex and bilateral supplementary motor areas. For the exercise of ipsilateral hand of 7 stroke patients, contralateral sensorimotor cortex was weakly activated, but ipsilateral posterial parietal cortex was obviously activated, and the activation of cerebrum was observed in 3 of them. For the other two patients, bilateral sensorimotor cortexes were activated during the exercise of ipsilateral hand, and the ipsilateral activated area was greater than the controlateral one. The exercise of contralateral hand activated contralateral sensorimotor cortex, posterior parietal cortex and contralateral supplementary motor area, and no obvious ipsilateral activated area was observed. ② Results of DTI examination: The anisotropic values of the infarcted area were obviously lower than those of the contralateral part (t=4.570, P < 0.01). the anisotropic value of the infarcted area were obviously was obviously correlated with bilateral muscle strength (t=0.888, P < 0.05). ③ Results of the examination for corticospinal tracts: The reconstruction of bilateral corticospinal tracts, contralateral anatomic form were generally identical with those of normal subjects, the consistency of each continuous form from anterior central gyrus downward to internal capsule to bridge of varolius and bulbus medullae. Because of the involvement of infarcted area to different extent, ipsilateral corticospinal tract was manifested by the interruption of succession and loss of consistency of anatomic structural form. The severity for the injury of corticospinal tract was markedly correlated with the muscle strength of the ipsilateral hand (r=0.888, P < 0.05). CONCLUSION: ① The MRI manifestations of stroke patients during the exercise of affected hand are different from those of normal subjects, suggesting that there is compensation and reconstruction of brain function. ② DTI examination is good for the judgement of the correlation between the damaged severity of infarction and muscle strength. ③ The damaged severity of corticospinal tracts is correlated with muscle strength, and it can be used to judge the prognosis of rehabilitative treatment. | Ziqian Chen Hui Xiao Biyun Zhang Gennian Qian Ping Ni Xizhang Yang | 2006 | Neural Regeneration Research2006，1，1： | 4 |
| 5 | Characters of MR diffusion tensor imaging in cerebral ischemic corticospinal tract injury显示文摘BACKGROUND: Diffusion tensor imaging (DTI) is one of the noninvasive methods to study the morphological structure of brain white matter fibrous bands in vivo, and it has been applied primarily in clinic. DTI is acknowledged as the more effective imaging method to diagnose ultra-acute and/or acute cerebral infarction. OBJECTIVE: To observe the anisotropic characters of cerebral white matter fibrous bands in patients with ischemic stroke by using DTI, and investigate the correlation between the damage of corticospinal tract and muscle strength in patients with ischemic stroke at acute period. DESIGN: A case-control observation. SETTING: Department of Medical Imaging, Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA. PARTICIPANTS: Nine inpatients with injury of motor function induced by acute ischemic stroke (patient group) at 6 hours to 2 weeks after the attack were selected from the Department of Neurology, Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA from September 2005 to March 2006, and they all accorded with the present diagnostic standard for cerebrovascular disease in China. There were 5 males and 4 females, aged 16-87 years. At the same time, nine healthy right-handed physical examinees matched by age and sex with the patients were taken as the control group, and they all had no nervous disease, mental diseases, cerebrovascular abnormalities and injury history, etc. All the subjects were informed with the detected items and agreed to participate in the study. METHODS: All the 9 patients with ischemic stroke at acute period and 9 healthy subjects were examined with MRI, T1 weighted imaging, T2 weighted imaging and DTI. And the data were processed offline with dTV.II software, the images of fractional anisotropy and directional encoded color (DEC) were obtained, and the three-dimensional fibrous band images of bilateral corticospinal tracts were reconstructed. In the control group, the values of fractional anisotropy of main white matter fibrous bands were measured in the region of interest (ROI) of the anterior limb, knee and posterior limb of internal capsule. In the patient group, the values of fractional anisotropy of white matter were measured in the infarcted sites and corresponding contralateral sites of the patients. The ROI was set in bilateral cerebral peduncles to reconstruct three-dimensionally the bilateral corticospinal tracts. The muscle strength of the affected hand was assessed with Brunnstorm standard in the stroke patients. MAIN OUTCOME MEASURES: The characters of DTI and images of the value of fractional anisotropy, and the manifestations of three-dimensional corticospinal tracts were observed in the two groups. RESULTS: All the data from the 9 patients and 9 healthy volunteers were involved in the analysis of results. ① In the control group, the white matter and gray matter could be distinguished clearly in the image of fractional anisotropic values, the fibers of different directions were shown by different colors in DEC picture, which clearly demonstrated the normal anatomic structure and direction of white matter fibers. In the patient group, the infarctions occurred in the gray matter or white matter could be distinguished in the images of fractional anisotropic values, DEC picture could clearly show the direct influence of the infarcted site on the white matter fibers. The fractional anisotropic values in different white matter structure of the same side were significantly different in the control group (t=3.12, P < 0.05), and the reconstructed images fractional anisotropic values and DEC picture could show most of the main white matter fibrous bands. The fractional anisotropic values of the infarcted sites were significantly lower than the contralateral ones in the patient group (t=5.570, P < 0.01). ② The reconstructed bilateral corticospinal tracts showed that the anatomic forms of the contralateral corticospinal tract of the patients were almost identical to those of normal people, it started from precentral gyrus, downward to the nternal capsule, and extended to pontine and medulla oblongata, each fibrous band was continuous, and the form had good consistency. Because of the involvement of infarction of different severity, the ipsilateral corticospinal tract manifested as continuous interruption and the loss of consistent anatomic structural form. The involved severity of corticospinal tract had significant correlation with that of muscle strength of the ipsilateral hand (r=1.30, P < 0.01). CONCLUSION: ① DTI can display the direction and distribution of cerebral white matter fibrous bands. ② DTI images of fractional anisotropic values and DEC can show the directions and anisotropic degree of white matter fibers in the infarcted sites of stroke patients. ③ The three-dimensional images of fibrous bands can show the conditions of pyramidal tracts more directly. ④ The damaged severity of corticospinal tracts is correlated with that of muscle strength. | Ziqian Chen Ping Ni Hui Xiao Youqiang Ye Gennian Qian Shangwen Xu Xizhang Yang Jinhua Chen Biyun zhang | 2006 | Neural Regeneration Research2006，1，2： | 3 |
| 6 | Changes in brain function and anatomical structure following treatment of hyperbaric oxygen for visual pathway abnormalities in 16 cases Evaluation of functional magnetic resonance imaging combined with diffusion tensor imaging显示文摘BACKGROUND: There is a growing research focus on the combination of blood oxygenation level dependent functional magnetic resonance imaging (BOLD-fMRI) and diffusion tensor imaging (DTI) to evaluate visual cortical function and structural changes in the cerebrum,as well as morphological changes to the white matter fiber tracks,after visual pathway lesions. However,the combined application of BOLD-fMRI and DTI in treating of visual pathway abnormalities still requires further studies. OBJECTIVE: To observe and evaluate the effects of hyperbaric oxygen on visual pathway abnormalities,and to evaluate the characteristics of cerebral function and anatomic structural changes by using BOLD-fMRI combined with DTI technique. DESIGN: Case contrast observation. SETTING: Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA. PARTICIPANTS: Sixteen patients (9 males and 7 females,15-77 years old) with lateral or bilateral visual disorder induced by visual pathway lesions were selected from the Department of Neurology,Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA from January 2006 to May 2007. These patients comprised the lesion group. Measures of interventional therapy: hyperbaric oxygen of two normal atmospheres for three courses (10 d/course) and routine internal medicine treatment. In addition,12 healthy subjects of similar sex and age to the lesion group were regarded as the control group. The control group underwent routine ophthalmological and ocular fundus examinations; diagnostic results were normal. The experiment received confirmed consent from the local ethic committee,and all patients provided informed consent. METHODS: BOLD-fMRI and DTI manifestations in the lesion group were observed before and after hyperbaric oxygen intervention,and the results were compared with the control group. The subjects were positioned on their back,and BOLD-fMRI images were collected with the following GRE EPI sequence: TR = 2 000 ms,TE = 40 ms,layer thickness = 5 mm,and 20-layer successive scanning to cover the whole brain. While,DTI images were collected with SE EPI sequence of single excitation: TR=10 000 ms,TE = 112 ms,layer thickness = 4 mm,layer spacing = 0.5 mm,and a 30-layer successive scanning,matrix = 128×128. A diffusion gradient was applied at 13 directions,and one layer without diffusion weighted imaging was collected at b =1 000 s/mm2. Numbers of activated voxels in cortical-activated regions,and fractional anisotropy in bilateral cerebral optical radiation regions,were calculated. Displacement,continuity,and destruction of fibrous tracts were analyzed. MAIN OUTCOME MEASURES: Results of BOLD-fMRI and DTI examinations. RESULTS: All 16 patients and 12 controls were included in the final analysis. ① Numbers of activated voxels through the use of BOLD-fMRI: prior to hyperbaric oxygen therapy,the number of activated voxels in the bilateral cortex of occipital lobe were significantly less in the lesion group than in the control group (t =3.23,P < 0.01). In addition,the number of activated voxels significantly increased after treatment compared to before treatment (t = 2.46,P < 0.05). ② Fractional anisotropy in optical radiation regions of bilateral cerebrum: fractional anisotropy in the lesion group was significantly less than the control group (t =2.89,P < 0.05). In addition,fractional anisotropy after treatment was significantly higher than before treatment (t = 2.48,P < 0.05). Moreover,fractional anisotropy of optical neuropathy was significantly higher in 6 patients in the lesion group than the occipital lobe optical central lesion (t = 2.35,P < 0.05). CONCLUSION: BOLD-fMRI combined with DTI can indicate the occurrence,development,and therapeutic course of action for optical pathway lesions. The results acquired from these methods can provide information for function and structure,which can provide reliable verification in the treatment of cerebral function. | Ziqian Chen Ping Ni Hui Xiao Jinhua Chen Gennian Qian Youqiang Ye Shangwen Xu Jinliang Wang Xizhang Yang | 2008 | Neural Regeneration Research2008，3，2： | 2 |
| 7 | Constructions for optimal( v,4, 1 ) optical orthogonal codes显示文摘 | Gennian ge Jianxing Yin | 2001 | IEEE trans on Information Theory2001，47，11： | 1 |
| 8 | Constructions for optimal(v,4,1)optical orthogonal codes显示文摘 | GE Gennian YIN Jianxing | | 0，，11： | 1 |
| 9 | Further combinatorial constructions for optimal frequency-hopping sequences显示文摘 | Gennian Ge Ryoh Fuji-Hara Ying Miao | 2006 | Journal of Combinatorial Theory A2006，113，： | 1 |
| 10 | Deterministic Construction of Compressed Sensing Matrices via Algebraic Curves显示文摘 | Li Shuxing Gao Fei Ge Gennian | 2012 | IEEE Transactions on Information Theory2012，58，8： | 1 |
| 11 | Uniform supersaturated design and its construction显示文摘 | Kaitai Fang Gennian Ge Minqian Liu | 2002 | Science in China Series A: Mathematics2002，，8： | 1 |
| 12 | Deterministic construction of sparse sensing matrices via finite geometry显示文摘 | LI Shuxing GE Gennian | 2014 | IEEE Transactions on Signal Processing2014，62，11： | 1 |
| 13 | Deterministic Construction of Compressed Sensing Matrices via Algebraic Curves显示文摘 | Li Shuxing Gao Fei Ge Gennian | 2012 | IEEE Transactions on Information Theory2012，58，8： | 1 |
| 14 | Observation of activation status of motor-related cortex of patients with acute ischemic stroke through functional magnetic resonance imaging显示文摘BACKGROUND: About more than three fourth of patients with stroke have motor dysfunction at different degrees, especially hand motor dysfunction. Functional magnetic resonance imaging (fMRI) provides very reliable visible evidence for studying central mechanism of motor dysfunction after stroke, and has guiding and applicable value for clinical therapy. OBJECTIVE: To observe the activation of motor-related cortex of patients with acute ischemic stroke with functional magnetic resonance imaging, and analyze the relationship between brain function reconstruction and motor restoration after stroke. DESIGN: A contrast observation. SETTING: Medical Imaging Center, Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA. PARTICIPANTS: Nine patients with acute ischemic stroke who suffered from motor dysfunction and received the treatment in the Fuzhou General Hospital of Nanjing Military Area Command of Chinese PLA between August and December 2005 were recruited, serving as experimental group. The involved patients including 5 male and 4 female, aged 16 to 87 years, all met the diagnostic criteria of cerebrovascular disease revised by The Fourth National Conference on Cerebrovascular Disease, mainly presenting paralysis in clinic, and underwent fMRI. Another 9 right handed persons matched in age and gender who simultaneously received healthy body examination were recruited, serving as control group. All the subjects were informed of the detected items. METHODS: ①Muscular strength of patients of the experimental group was evaluated according to Brunnstrom grading muscular strength(Grade Ⅰ-Ⅵ). ② Passive finger to finger motion was used as the mission (alternate style of quiescence, left hand motion and quiescence , right hand motion was repeated 3 times, serving as 1 sequence, 20 s per block and 20 s time interval . The whole process of scanning was 260 s), and subjects of 2 groups were given Bold-fMRI examination with GE1.5T double gradient 16-channel magnetic resonance imaging system. All the data were given off-line management, and fMRI was treated with SPM2 software. The activation of passive finger-to-finger motion-related cortex of subjects in 2 groups was observed. ③ Results of fMRI of subjects in 2 groups were compared. The size of activation region of brain and signal intensity were measured and unilateral index was calculated. The data of activation region of cerebral hemisphere of different sides at finger motion were given statistical analysis of unilateral index. Differences among unilateral indexes at hand motion were compared between intact and affected hands of patients in experimental group. The relationship between unilateral index and muscular strength of affected hands at affected hand motion in patients of the experimental group was performed Spearman correlation analysis. MAIN OUTCOME MEASURES: ① The activation of motion-related cortex passive finger-to-finger motion between handedness and non-handedness was detected with functional magnetic resonance imaging of subjects in 2 groups. ② Relationship between unilateral index and muscular strength of subjects of experimental group at affected hand motion. RESULTS: Nine patients with ischemic stroke and 9 controls all participated in the final result analysis. ① Passive fMRI detection results between handedness and non-handedness of controls: Right-handed finger-to-finger motion of subjects of control group mainly activated contralateral sensorimotor cortex, and left-handed finger-to-finger motion not only activated above-mentioned brain region, but also activated supplementary motor area (SMA) of contralateral brain region; ②In the experimental group, sensorimotor cortex of contralateral hemisphere was activated at affected hand motion, and homolateral posterior parietal cortex (PPC)was also obviously activated. Bilateral sensorimotor cortex was activated at affected hand motion in 2 patients, and homolateral activation area was larger than contralateral one. At intact hand motion, contralateral sensorimotor cortex was activated, but no obvious homolateral activation area was found. ③ Correlation of unilateral index with muscular strength: Passive finger-to-finger fMRI ( between affected and intact hands of subjects of experimental group: Unilateral index at passive single finger motion of affected and intact hand of subjects of experimental group was -0.018±0.01 and 0.319±0.187, respectively, with significant difference (t=4.059, P < 0.01). Unilateral index was significantly positively correlated with the muscular strength of affected hand at affected hand motion(r=0.834, P < 0.05). CONCLUSION: ① fMRI can objectively shows different activation states of motor cortex between patients with ischemic stroke and healthy controls, and brain functional compensation and recombination exist. Both primary sensorimotor cortex and SMA of bilateral hemispheres participant in affected hand motion, at the same time, parietal lobe and cortex of intact side also obviously participant in the affected hand motion. ②Correlation analysis of unilateral index and muscular strength of affected hand performed through fMRI can be used as an effective means to investigate the relationship between motion rehabilitation and brain functional recombination after stroke. | Ziqian Chen Hui Xiao Ping Ni Gennian Qian Shangwen Xu Xizhang Yang Youqiang Ye Jinhua Chen Biyun Zhang | 2006 | Neural Regeneration Research2006，1，3： | 1 |
| 15 | Combinatorial Characteriza- tions of One-Coincidence Frequence-Hopping Sequences 显示文摘 | Zhenfu Cao Gennian Ge Ying Miao | 2006 | Des Codes Crypt2006，41，： | 1 |
| 16 | Deterministic construction of sparse sensingmatricesviafinitegeometry显示文摘 | LI SHUXING GE GENNIAN | 2014 | IEEE Trans on Signal Processing2014，62，： | 1 |
| 17 | Some extremal results on hypergraph Turán problems显示文摘For two r-graphs T and H,let ex_(r)(n,T,H)be the maximum number of copies of T in an n-vertex H r-graph.The determination of the Turán number ex_(r)(n,T,H)has become the fundamental core problem in extremal graph theory ever since the pioneering work of Turán’s theorem was published in 1941.Although we have some rich results for the simple graph case,only sporadic results have been known for the hypergraph Turán problems.In this paper,we mainly focus on the function ex_(r)(n,T,H)when H is one of two different hypergraph extensions of the complete bipartite graph K_(s,t).The first extension is the complete bipartite r-graph K^((r))_(s,t),which was introduced by Mubayi and Verstraëte(2004).Using the powerful random algebraic method,we show that if s is sufficiently larger than t,then ex_(r)(n,T,K^((r))_(s,t))=Ω(n^(v−e/t)),where T is an r-graph with v vertices and e edges.In particular,when T is an edge or some specified complete bipartite r-graph,we can determine their asymptotics.The second important extension is the complete r-partite r-graph K^((r))_(s1,s2,…,sr,)which has been widely studied.When r=3,we provide an explicit construction giving ex_(3)(n,K^((3))_(2,2,7))≥1/27n19/7+o(n19/7).Our construction is based on the norm graph,and improves the lower boundΩ(n73/27)obtained by the probabilistic method. | Zixiang Xu Tao Zhang Gennian Ge | 2022 | Science China Mathematics2022，65，8： | 0 |
| 18 | Some intriguing upper bounds for separating hash families显示文摘An N ×n matrix on q symbols is called {w_1,...,w_t}-separating if for arbitrary t pairwise disjoint column sets C_1,..., C_t with |C_i|=w_i for 1 ≤i≤t, there exists a row f such that f(C_1),...,f(C_t) are also pairwise disjoint, where f(C_i) denotes the collection of componentn of C_i restricted to row f. Given integers N, q and w_1,...,w_t, denote by C(N,q,{w_1,...,w_t}) the maximal a such that a corresponding matrix does exist.The determination of C(N,q,{w_1,...,w_t}) has received remarkable attention during the recent years. The main purpose of this paper is to introduce two novel methodologies to attack the upper bound of C(N, q, {w_1,...,w_t}).The first one is a combination of the famous graph removal lemma in extremal graph theory and a Johnson-type recursive inequality in coding theory, and the second onc is the probabilistic method. As a consequence, we obtain several intriguing upper bounds for some parameters of C(N,q,{w_1,...,w_t}), which significantly improve the previously known results. | Gennian Ge Chong Shangguan Xin Wang | 2019 | Science China Mathematics2019，62，2： | 0 |
| 19 | Inverse problems of the Erdos-Ko-Rado type theorems for families of vector spaces and permutations显示文摘Ever since the famous Erd os-Ko-Rado theorem initiated the study of intersecting families of subsets,extremal problems regarding intersecting properties of families of various combinatorial objects have been extensively investigated.Among them,studies about families of subsets,vector spaces and permutations are of particular concerns.Recently,we proposed a new quantitative intersection problem for families of subsets:For F([n]k),define its total intersection number as I(F)=ΣF1;F2∈F|F1∩F2|.Then,what is the structure of F when it has the maximal total intersection number among all the families in([n]k)with the same family size?In a recent paper,Kong and Ge(2020)studied this problem and characterized extremal structures of families maximizing the total intersection number of given sizes.In this paper,we consider the analogues of this problem for families of vector spaces and permutations.For certain ranges of family sizes,we provide structural characterizations for both families of subspaces and families of permutations having maximal total intersection numbers.To some extent,these results determine the unique structure of the optimal family for some certain values of jFj and characterize the relationship between having the maximal total intersection number and being intersecting.Besides,we also show several upper bounds on the total intersection numbers for both families of subspaces and families of permutations of given sizes. | Xiangliang Kong Yuanxiao Xi Bingchen Qian Gennian Ge | 2022 | Science China Mathematics2022，65，5： | 0 |
| 20 | Longitudial observation of dynamic changes in cortical function and white matter fibrous structure of patients with visual pathway lesions by blood oxygenation level dependent-functional magnetic resonance imaging combined with diffusion tensor imaging显示文摘BACKGROUND: Functional magnetic resonance imaging (fMRI) is initially used for visual cortex location. However, the application of fMRI in investigating the development of visual pathway lesions needs to be further observed. OBJECTIVE: This study is to longitudially observe the dynamic changes in cortical function and white matter fibrous structure of patients with visual pathway lesions by blood oxygenation level dependent-functional magnetic resonance imaging (BOLD-fMRI) combined with diffusion tensor imaging (DTI), and to analyze the characteristics of brain function and structural recombination at convalescent period of lesions. DESIGN: Randomized controlled observation. SETTING: Department of Radiology, the General Hospital of Nanjing Military Area Command of Chinese PLA. PARTICIPANTS: Eight patients with unilateral or bilateral visual disorder caused by visual pathway lesions, who admitted to Department of Radiology, the General Hospital of Nanjing Military Area Command of Chinese PLA from January to September 2006 were involved, and served as experimental subjects. The patients, 6 males and 2 females, were aged 16-67 years. They had visual disorder confirmed by clinical examination, i.e. visual pathway lesion, which was further diagnosed by MR or CT. Another 12 subjects generally matching to those patients of experimental group in gender, age and sight, who received health examination in synchronization were involved and served as controls. The subjects had no history of eye diseases. Their binocular visual acuity (or corrected visual acuity) was over 1.0. Both routine examination of ophthalmology and examination of fundus were normal. Informed consents of detected items were obtained from all the subjects. METHODS: Signa Excite HD 1.5T magnetic resonance imaging system with 16 passages (GE Company, USA) and coil with 8 passages were used; brain functional stimulus apparatus (SAV-8800. Meide Company) was used for showing experimental mission. At the early stage and convalescent period of lesions, the patients with visual pathway lesion were examined by BOLD-fMRI combined with DTI, respectively, and brain activation volume, optic radiation anatomical structure and fractional anisotropy (FA) value were compared before and after symptomatic treatment under the stimulation to both eyes. The above-mentioned indexes were observed and compared between experimental and control groups. MAIN OUTCOME MEASURES: BOLD-fMRI and DTI manifestations before and after treatment in the experimental group and control group. RESULTS: All the 8 patients and 12 healthy subjects participated in the final analysis. ①BOLD-fMRI manifestation: Bilateral occipital lobes and calcarine gyri of control subjects were obviously activated. The activation volume of striate cortex under the stimulation to two eyes was obviously reduced in the experimental subjects than in the control subjects (P < 0.05). After treatment, the amount of activated pixel in the stimulated cortex was increased, and the activation area was expanded. ② DTI results: Bilateral optic radiation of healthy controls could be traced in the subcortex. Complete optic radiation of patients with visual pathway lesion could be shown. There was no significant difference in optic radiation between experimental subjects and healthy controls. No significant difference in optic radiation was foundbefore and after observation, either (P > 0.05). In 4 patients with occipital lobe and optical center lesions, optic radial fiber was partially interrupted and tenuous, displacement could be found, and FA value was obviously decreased; After treatment, optic radial fiber bundle recovered to some extent, and FA value was also increased. CONCLUSION: BOLD-fMRI and DTI explain the development of lesion from the aspect of cortical function and fibrous anatomy. It has important significance for investigating the recombination of cortical function area following visual pathway lesion. | Hui Xiao Ziqian Chen Gennian Qian Ping Ni Youqiang Ye Jinhua Chen | 2007 | Neural Regeneration Research2007，2，8： | 0 |
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