The oral microbiome is an important part of the human microbiome. The oral cavity contains several significantly different niches with distinct microbial communities. A wide range of microorganisms ...inhabit the human oral cavity, including bacteria, fungi, viruses, archaea and protozoa. These microorganisms form a complex ecological community that influences oral and systemic health. The most prevalent oral diseases, dental caries and periodontal diseases, are microbiota-associated diseases. Moreover, increasing evidences have supported that many systemic diseases are associated with disturbances in the oral ecosystem, such as diabetes, cardiovascular diseases and tumors. The current control of dental plaque-related diseases is nonspecific and is centered on the removal of plaque by mechanical means. Due to this realization about the oral microbiome, several new methods based on the modulation of the microbiome that aim at maintaining and reestablishing a healthy oral ecosystem have been developed.
The Wiener polarity number (which, nowadays, known as the Wiener polarity index and usually denoted by Wp) was devised by the chemist Harold Wiener, for predicting the boiling points of alkanes. The ...index Wp of chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices (carbon atoms) at distance 3. The inverse problems based on some well-known topological indices have already been addressed in the literature. The solution of such inverse problems may be helpful in speeding up the discovery of lead compounds having the desired properties. This paper is devoted to solving a stronger version of the inverse problem based on Wiener polarity index for chemical trees. More precisely, it is proved that for every integer t ∈ {n - 3, n - 2,…,3n - 16, 3n - 15}, n ≥ 6, there exists an n-vertex chemical tree T such that Wp(T) = t.
Cographs is a well-known class of graphs in graph theory, which can be generated from a single vertex by applying a series of complement (or equivalently join operations) and disjoint union ...operations. The distance spectrum of graphs is a rather active topic in spectral graph theory these years. This paper denotes to revealing some properties for the distance spectrum of cographs. More precisely, we present an algorithm, using <inline-formula> <tex-math notation="LaTeX">O(n) </tex-math></inline-formula> time and space, to diagonalize the distance matrix of cographs, from which one can deduce a diagonal matrix congruent to matrix <inline-formula> <tex-math notation="LaTeX">D + \lambda I </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> is the distance matrix of a cograph, <inline-formula> <tex-math notation="LaTeX">\lambda </tex-math></inline-formula> is a real number, and <inline-formula> <tex-math notation="LaTeX">I </tex-math></inline-formula> is the identity matrix. Besides, we also give some applications of such algorithm about the inertia of distance matrix of complete multipartite graphs.
The eigenvalues of
G
are denoted by
λ
1
(
G
)
,
λ
2
(
G
)
,
…
,
λ
n
(
G
)
, where
n
is the order of
G
. In particular,
λ
1
(
G
)
is called the spectral radius of
G
,
λ
n
(
G
)
is the least eigenvalue ...of
G
, and the spread of
G
is defined to be the difference between
λ
1
(
G
)
and
λ
n
(
G
)
. Let
U
(
n
)
be the set of
n
-vertex unicyclic graphs, each of whose vertices on the unique cycle is of degree at least three. We characterize the graphs with the
k
th maximum spectral radius among graphs in
U
(
n
)
for
k
=
1
if
n
≥
6
,
k
=
2
if
n
≥
8
, and
k
=
3
,
4
,
5
if
n
≥
10
, and the graph with minimum least eigenvalue (maximum spread, respectively) among graphs in
U
(
n
)
for
n
≥
6
.
The contribution of metabolic factors on the severity of osteoarthritis (OA) is not fully appreciated. This study aimed to define the effects of hyper cholesterolemia on the progression of OA. A ...polipoprotein E‐deficient (ApoE−/−) mice and rats with diet‐induced hypercholesterolemia (DIHC) rats were used to explore the effects of hyper cholesterolemia on the progression of OA. Both models exhibited OA‐like changes, characterized primarily by a loss of proteoglycans, collagen and aggrecan degradation, osteophyte formation, changes to subchondral bone architecture, and cartilage degradation. Surgical destabilization of the knees resulted in a dramatic increase of degradative OA symptoms in animals fed a high‐cholesterol diet compared with controls. Clinically relevant doses of free cholesterol resulted in mitochondrial dysfunction, overproduction of reactive oxygen species (ROS), and increased expression of degenerative and hypertrophic markers in chondrocytes and breakdown of the cartilage matrix. We showed that the severity of diet‐induced OA changes could be attenuated by treatment with both atorvastatin and a mitochondrial targeting antioxidant. The protective effects of the mitochondrial targeting antioxidant were associated with suppression of oxidative damage to chondrocytes and restoration of extracellular matrix homeostasis of the articular chondrocytes. In summary, our data show that hypercholesterolemia precipitates OA progression by mitochondrial dysfunction in chondrocytes, in part by increasing ROS production and apoptosis. By addressing the mitochondrial dysfunction using antioxidants, we were able attenuate the OA progression in our animal models. This approach may form the basis for novel treatment options for this OA risk group in humans.—Farnaghi, S., Prasadam, I., Cai, G., Friis, T., Du, Z., Crawford, R., Mao, X., Xiao, Y. Protective effects of mitochondria‐targeted antioxidants and statins on cholesterolinduced osteoarthritis. FASEB J. 31, 356–367 (2017) www.fasebj.org
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Compromised bone quality and/or healing in osteoporosis are recognised risk factors for impaired dental implant osseointegration. This study examined the effects of (1) experimentally ...induced osteoporosis on titanium implant osseointegration and (2) the effect of modified implant surface topography on osseointegration under osteoporosis-like conditions. Machined and micro-roughened surface implants were placed into the maxillary first molar root socket of 64 ovariectomised and sham-operated Sprague-Dawley rats. Subsequent histological and SEM observations showed tissue maturation on the micro-rough surfaced implants in ovariectomised animals as early as 3days post-implantation. The degree of osseointegration was also significantly higher around the micro-rough implants in ovariectomised animals after 14days of healing although by day 28, similar levels of osseointegration were found for all test groups. The micro-rough implants significantly increased the early (day 3) gene expression of alkaline phosphatase, osteocalcin, receptor activator of nuclear factor kappa-B ligand and dentin matrix protein 1 in implant adherent cells. By day 7, the expression of inflammatory genes decreased while the expression of the osteogenic markers increased further although there were few statistically significant differences between the micro-rough and machined surfaces. Osteocyte morphology was also affected by estrogen deficiency with the size of the cells being reduced in trabecular bone. In conclusion, estrogen deficiency induced osteoporotic conditions negatively influenced the early osseointegration of machined implants while micro-rough implants compensated for these deleterious effects by enhancing osteogenic cell differentiation on the implant surface.
Lower bone density, poor bone quality and osseous microstructural changes are all features characteristic of osteoporosis that may impair the osseointegration of dental implants. Using a clinically relevant trabecular bone model in the rat maxilla, we demonstrated histologically that the negative effects of surgically-induced osteoporosis on osseointegration could be ameliorated by the biomaterial’s surface topography. Furthermore, gene expression analysis suggests this may be a result of enhanced osteogenic cell differentiation on the implant surface.
The atom-bond connectivity (ABC) index of a graph
G
is defined as
ABC
(
G
)
=
∑
u
v
∈
E
(
G
)
d
u
+
d
v
−
2
d
u
d
v
,
where
E
(
G
)
is the edge set and
d
u
is the degree of vertex
u
of
G
. We give ...the best upper bound for the ABC index of trees with a perfect matching, and characterize the unique extremal tree, which is a molecular tree. We also give upper bounds for the ABC index of trees with fixed number of vertices and maximum degree, and of molecular trees with fixed numbers of vertices and pendent vertices, and characterize the extremal trees.
Objectives: Osteoporosis is known to impair the process of implant osseointegration. The recent discovery that statins (HMG‐CoA reductase inhibitors) act as bone anabolic agents suggests that statins ...can be used as potential agents in the treatment of osteoporosis. Therefore, we hypothesized that statins will promote osteogenesis around titanium implants in subjects with osteoporosis.
Material and methods: Fifty‐four female Sprague Dawley rats, aged 3 months old, were randomly divided into three groups: Sham‐operated group (SHAM; n=18), ovariectomized group (OVX; n=18), and ovariectomized with Simvastatin treatment group (OVX+SIM; n=18). Fifty‐six days after being ovariectomized (OVX), screw‐shaped titanium implants were inserted into the tibiae. Simvastatin was administered orally at 5 mg/kg each day after the placement of the implant in the OVX+SIM group. The animals were sacrificed at either 28 or 84 days after implantation and the undecalcified tissue sections were obtained. Bone‐to‐implant contact (BIC) and bone area (BA) within the limits of implant threads were measured around the cortical (zone A) and cancellous (zone B) bone regions. Furthermore, bone density (BD) of zone B in a 500 μm wide zone lateral to the implants was also measured.
Results: There were no significant differences in BIC and BA measurements in zone A in any of the three groups at either 28 or 84 days after implantation (P>0.05). By contrast, in zone B, significant differences in the measurement of BIC, BA, and BD were observed at 28 and 84 days between all three groups. Bone healing decreased with lower BIC, BA, and BD around implant in OVX group compared with other two groups, and Simvastatin reversed the negative effect of OVX on bone healing around implants with the improvement of BIC, BA, and BD in zone B.
Conclusion: Osteoporosis can significantly influence bone healing in the cancellous bone around titanium implants and Simvastatin was shown to significantly improve the osseointegration of pure titanium implants in osteoporotic rats.
We analyse the roots of the polynomial
x
n
−
px
n
−1
−
qx
− 1 for
p
≽
q
≽ 1. This is the characteristic polynomial of the recurrence relation
F
k,p,q
(
n
) =
pF
k,p,q
(
n
− 1) +
qF
k,p,q
(
n
−
k
+ 1) ...+
F
k,p,q
(
n
−
k
) for
n
≽
k
, which includes the relations of several particular sequences recently defined. In the end, a matricial representation for such a recurrence relation is provided.
Further developments of basic trigonometric power sums Du, Zhibin; da Fonseca, Carlos M.; Kowalenko, Victor
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas,
07/2023, Letnik:
117, Številka:
3
Journal Article
Recenzirano
In this article we present some additional and complementary remarks to an earlier paper on finite trigonometric power sums. First, we extend the results to include an offset angle in the ...trigonometric power in the summand. Next we include more complicated phase factors accompanying the trigonometric powers. Despite their more intricate nature, we find that these trigonometric power sums are still rational. Finally, we not only prove the conjecture raised in the earlier paper, but also generalize it.
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